aboutsummaryrefslogtreecommitdiff
path: root/src/algebra
diff options
context:
space:
mode:
authordos-reis <gdr@axiomatics.org>2009-05-18 23:46:53 +0000
committerdos-reis <gdr@axiomatics.org>2009-05-18 23:46:53 +0000
commitaa129f3b4eaacbeae2837fb7e5c67a1a1a373eaa (patch)
tree2a10e3ef795b0e2625f642cf2d1d47c7e695a88e /src/algebra
parent7f0313f8c6cce367c51cf5bb6bc8c073a466191b (diff)
downloadopen-axiom-aa129f3b4eaacbeae2837fb7e5c67a1a1a373eaa.tar.gz
* algebra/curve.spad.pamphlet: Use literal symbols.
* algebra/defintef.spad.pamphlet: Likewise. * algebra/defintrf.spad.pamphlet: Likewise. * algebra/divisor.spad.pamphlet: Likewise. * algebra/efstruc.spad.pamphlet: Likewise. * algebra/exprode.spad.pamphlet: Likewise. * algebra/fspace.spad.pamphlet: Likewise. * algebra/intaf.spad.pamphlet: Likewise. * algebra/intef.spad.pamphlet: Likewise. * algebra/integrat.spad.pamphlet: Likewise. * algebra/intpm.spad.pamphlet: Likewise. * algebra/laplace.spad.pamphlet: Likewise. * algebra/limitps.spad.pamphlet: Likewise. * algebra/liouv.spad.pamphlet: Likewise. * algebra/odeef.spad.pamphlet: Likewise. * algebra/oderf.spad.pamphlet: Likewise. * algebra/rdeef.spad.pamphlet: Likewise. * algebra/symbol.spad.pamphlet: Likewise. * algebra/transsolve.spad.pamphlet: Likewise.
Diffstat (limited to 'src/algebra')
-rw-r--r--src/algebra/curve.spad.pamphlet4
-rw-r--r--src/algebra/defintef.spad.pamphlet18
-rw-r--r--src/algebra/defintrf.spad.pamphlet4
-rw-r--r--src/algebra/divisor.spad.pamphlet2
-rw-r--r--src/algebra/efstruc.spad.pamphlet100
-rw-r--r--src/algebra/exprode.spad.pamphlet2
-rw-r--r--src/algebra/fspace.spad.pamphlet16
-rw-r--r--src/algebra/intaf.spad.pamphlet18
-rw-r--r--src/algebra/intef.spad.pamphlet24
-rw-r--r--src/algebra/integrat.spad.pamphlet12
-rw-r--r--src/algebra/intpm.spad.pamphlet4
-rw-r--r--src/algebra/laplace.spad.pamphlet12
-rw-r--r--src/algebra/limitps.spad.pamphlet4
-rw-r--r--src/algebra/liouv.spad.pamphlet4
-rw-r--r--src/algebra/odeef.spad.pamphlet2
-rw-r--r--src/algebra/oderf.spad.pamphlet4
-rw-r--r--src/algebra/rdeef.spad.pamphlet14
-rw-r--r--src/algebra/strap/SYMBOL.lsp4
-rw-r--r--src/algebra/symbol.spad.pamphlet2
-rw-r--r--src/algebra/transsolve.spad.pamphlet2
20 files changed, 127 insertions, 125 deletions
diff --git a/src/algebra/curve.spad.pamphlet b/src/algebra/curve.spad.pamphlet
index 11d82292..37d330ee 100644
--- a/src/algebra/curve.spad.pamphlet
+++ b/src/algebra/curve.spad.pamphlet
@@ -211,8 +211,8 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where
d := commonDenominator(coordinates(w := integralBasis()))::RF
n := #w
vars := [concat(string u, string i)::SY for i in 1..n]
- x := "%%dummy1"::SY
- y := "%%dummy2"::SY
+ x := '%%dummy1
+ y := '%%dummy2
select_!(zero?(degree(#1, x)) and zero?(degree(#1, y)),
lexGroebner([v::P - UPUP2P(lift(d * w.i), x::P, y::P)
for v in vars for i in 1..n], concat([x, y], vars)))
diff --git a/src/algebra/defintef.spad.pamphlet b/src/algebra/defintef.spad.pamphlet
index 9426ab08..e4fb77e3 100644
--- a/src/algebra/defintef.spad.pamphlet
+++ b/src/algebra/defintef.spad.pamphlet
@@ -108,9 +108,9 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where
(z := isExpt p) case "failed" => "failed"
k := z.var
-- functions with no real zeros
- is?(k, "exp"::SE) or is?(k, "acot"::SE) or is?(k, "cosh"::SE) => false
+ is?(k, 'exp) or is?(k, 'acot) or is?(k, 'cosh) => false
-- special case for log
- is?(k, "log"::SE) =>
+ is?(k, 'log) =>
(w := moreThan(b, 1)) case "failed" or not(w::B) => w
moreThan(-a, -1)
"failed"
@@ -144,21 +144,21 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where
nullary? operator kk => false
f := first argument kk
-- functions which are defined over all the reals:
- is?(kk, "exp"::SE) or is?(kk, "sin"::SE) or is?(kk, "cos"::SE)
- or is?(kk, "sinh"::SE) or is?(kk, "cosh"::SE) or is?(kk, "tanh"::SE)
- or is?(kk, "sech"::SE) or is?(kk, "atan"::SE) or is?(kk, "acot"::SE)
- or is?(kk, "asinh"::SE) => checkForPole(f, x, k, a, b)
+ is?(kk, 'exp) or is?(kk, 'sin) or is?(kk, 'cos)
+ or is?(kk, 'sinh) or is?(kk, 'cosh) or is?(kk, 'tanh)
+ or is?(kk, 'sech) or is?(kk, 'atan) or is?(kk, 'acot)
+ or is?(kk, 'asinh) => checkForPole(f, x, k, a, b)
-- functions which are defined on (-1,+1):
- is?(kk, "asin"::SE) or is?(kk, "acos"::SE) or is?(kk, "atanh"::SE) =>
+ is?(kk, 'asin) or is?(kk, 'acos) or is?(kk, 'atanh) =>
((w := checkForPole(f, x, k, a, b)) case "failed") or (w::B) => w
((w := posit(f - 1, x, k, a, b)) case "failed") or (w::B) => w
negat(f + 1, x, k, a, b)
-- functions which are defined on (+1, +infty):
- is?(kk, "acosh"::SE) =>
+ is?(kk, 'acosh) =>
((w := checkForPole(f, x, k, a, b)) case "failed") or (w::B) => w
negat(f - 1, x, k, a, b)
-- functions which are defined on (0, +infty):
- is?(kk, "log"::SE) =>
+ is?(kk, 'log) =>
((w := checkForPole(f, x, k, a, b)) case "failed") or (w::B) => w
negat(f, x, k, a, b)
"failed"
diff --git a/src/algebra/defintrf.spad.pamphlet b/src/algebra/defintrf.spad.pamphlet
index dcd67691..421f1aa4 100644
--- a/src/algebra/defintrf.spad.pamphlet
+++ b/src/algebra/defintrf.spad.pamphlet
@@ -97,7 +97,7 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where
error "integrate: last argument must be 'noPole'"
computeInt(k, f, a, b, eval?) ==
- is?(f, "integral"::SE) => "failed"
+ is?(f, 'integral) => "failed"
if not eval? then f := mkLogPos f
((ib := findLimit(f, k, b, "left", eval?)) case "failed") or
((ia := findLimit(f, k, a, "right", eval?)) case "failed") => "failed"
@@ -116,7 +116,7 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where
mkLogPos f ==
lk := empty()$List(K)
lv := empty()$List(F)
- for k in kernels f | is?(k, "log"::SE) repeat
+ for k in kernels f | is?(k, 'log) repeat
if (v := mkKerPos k) case F then
lk := concat(k, lk)
lv := concat(v::F, lv)
diff --git a/src/algebra/divisor.spad.pamphlet b/src/algebra/divisor.spad.pamphlet
index c0fbbc1f..c256a122 100644
--- a/src/algebra/divisor.spad.pamphlet
+++ b/src/algebra/divisor.spad.pamphlet
@@ -658,7 +658,7 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where
hyper:UP := uhyper::UP
gen:Z := ((degree(hyper)::Z - 1) exquo 2)::Z -- genus of the curve
- dvd:O := "div"::Symbol::O
+ dvd:O := 'div::O
zer:O := 0::Z::O
makeDivisor : (UP, UP, R) -> %
diff --git a/src/algebra/efstruc.spad.pamphlet b/src/algebra/efstruc.spad.pamphlet
index fe6d0bb3..320842e5 100644
--- a/src/algebra/efstruc.spad.pamphlet
+++ b/src/algebra/efstruc.spad.pamphlet
@@ -127,8 +127,6 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
SMP ==> SparseMultivariatePolynomial(R, K)
REC ==> Record(func:F, kers: List K, vals:List F)
U ==> Union(vec:Vector Q, func:F, fail: Boolean)
- POWER ==> "%power"::SY
- NTHR ==> "nthRoot"::SY
Exports ==> with
normalize: F -> F
@@ -159,6 +157,8 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
++ tanQ(q,a) is a local function with a conditional implementation.
Implementation ==> add
+ macro POWER == '%power
+ macro NTHR == 'nthRoot
import TangentExpansions F
import IntegrationTools(R, F)
import IntegerLinearDependence F
@@ -242,35 +242,35 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
[f, empty(), empty()]
deprel(ker, k, x) ==
- is?(k, "log"::SY) or is?(k, "exp"::SY) =>
+ is?(k, 'log) or is?(k, 'exp) =>
qdeprel([differentiate(g, x) for g in toY ker],
differentiate(ktoY k, x))
- is?(k, "atan"::SY) or is?(k, "tan"::SY) =>
+ is?(k, 'atan) or is?(k, 'tan) =>
qdeprel([differentiate(g, x) for g in toU ker],
differentiate(ktoU k, x))
is?(k, NTHR) => rootDep(ker, k)
- comb? and is?(k, "factorial"::SY) =>
- factdeprel([x for x in ker | is?(x,"factorial"::SY) and x~=k],k)
+ comb? and is?(k, 'factorial) =>
+ factdeprel([x for x in ker | is?(x,'factorial) and x~=k],k)
[true]
ktoY k ==
- is?(k, "log"::SY) => k::F
- is?(k, "exp"::SY) => first argument k
+ is?(k, 'log) => k::F
+ is?(k, 'exp) => first argument k
0
ktoZ k ==
- is?(k, "log"::SY) => first argument k
- is?(k, "exp"::SY) => k::F
+ is?(k, 'log) => first argument k
+ is?(k, 'exp) => k::F
0
ktoU k ==
- is?(k, "atan"::SY) => k::F
- is?(k, "tan"::SY) => first argument k
+ is?(k, 'atan) => k::F
+ is?(k, 'tan) => first argument k
0
ktoV k ==
- is?(k, "tan"::SY) => k::F
- is?(k, "atan"::SY) => first argument k
+ is?(k, 'tan) => k::F
+ is?(k, 'atan) => first argument k
0
smpElem(p, l) ==
@@ -284,41 +284,41 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
empty?(args :List F := [realElem(a, l) for a in argument k]) => kf
z := first args
is?(k, POWER) => (zero? z => 0; exp(last(args) * log z))
- is?(k, "cot"::SY) => inv tan z
- is?(k, "acot"::SY) => atan inv z
- is?(k, "asin"::SY) => atan(z / sqrt(1 - z**2))
- is?(k, "acos"::SY) => atan(sqrt(1 - z**2) / z)
- is?(k, "asec"::SY) => atan sqrt(1 - z**2)
- is?(k, "acsc"::SY) => atan inv sqrt(1 - z**2)
- is?(k, "asinh"::SY) => log(sqrt(1 + z**2) + z)
- is?(k, "acosh"::SY) => log(sqrt(z**2 - 1) + z)
- is?(k, "atanh"::SY) => log((z + 1) / (1 - z)) / (2::F)
- is?(k, "acoth"::SY) => log((z + 1) / (z - 1)) / (2::F)
- is?(k, "asech"::SY) => log((inv z) + sqrt(inv(z**2) - 1))
- is?(k, "acsch"::SY) => log((inv z) + sqrt(1 + inv(z**2)))
- is?(k, "%paren"::SY) or is?(k, "%box"::SY) =>
+ is?(k, 'cot) => inv tan z
+ is?(k, 'acot) => atan inv z
+ is?(k, 'asin) => atan(z / sqrt(1 - z**2))
+ is?(k, 'acos) => atan(sqrt(1 - z**2) / z)
+ is?(k, 'asec) => atan sqrt(1 - z**2)
+ is?(k, 'acsc) => atan inv sqrt(1 - z**2)
+ is?(k, 'asinh) => log(sqrt(1 + z**2) + z)
+ is?(k, 'acosh) => log(sqrt(z**2 - 1) + z)
+ is?(k, 'atanh) => log((z + 1) / (1 - z)) / (2::F)
+ is?(k, 'acoth) => log((z + 1) / (z - 1)) / (2::F)
+ is?(k, 'asech) => log((inv z) + sqrt(inv(z**2) - 1))
+ is?(k, 'acsch) => log((inv z) + sqrt(1 + inv(z**2)))
+ is?(k, '%paren) or is?(k, '%box) =>
empty? rest args => z
kf
if has?(op := operator k, 'htrig) then iez := inv(ez := exp z)
- is?(k, "sinh"::SY) => (ez - iez) / (2::F)
- is?(k, "cosh"::SY) => (ez + iez) / (2::F)
- is?(k, "tanh"::SY) => (ez - iez) / (ez + iez)
- is?(k, "coth"::SY) => (ez + iez) / (ez - iez)
- is?(k, "sech"::SY) => 2 * inv(ez + iez)
- is?(k, "csch"::SY) => 2 * inv(ez - iez)
+ is?(k, 'sinh) => (ez - iez) / (2::F)
+ is?(k, 'cosh) => (ez + iez) / (2::F)
+ is?(k, 'tanh) => (ez - iez) / (ez + iez)
+ is?(k, 'coth) => (ez + iez) / (ez - iez)
+ is?(k, 'sech) => 2 * inv(ez + iez)
+ is?(k, 'csch) => 2 * inv(ez - iez)
if has?(op, 'trig) then tz2 := tan(z / (2::F))
- is?(k, "sin"::SY) => 2 * tz2 / (1 + tz2**2)
- is?(k, "cos"::SY) => (1 - tz2**2) / (1 + tz2**2)
- is?(k, "sec"::SY) => (1 + tz2**2) / (1 - tz2**2)
- is?(k, "csc"::SY) => (1 + tz2**2) / (2 * tz2)
+ is?(k, 'sin) => 2 * tz2 / (1 + tz2**2)
+ is?(k, 'cos) => (1 - tz2**2) / (1 + tz2**2)
+ is?(k, 'sec) => (1 + tz2**2) / (1 - tz2**2)
+ is?(k, 'csc) => (1 + tz2**2) / (2 * tz2)
op args
--The next 5 functions are used by normalize, once a relation is found
depeval(f, lk, k, v) ==
- is?(k, "log"::SY) => logeval(f, lk, k, v)
- is?(k, "exp"::SY) => expeval(f, lk, k, v)
- is?(k, "tan"::SY) => taneval(f, lk, k, v)
- is?(k, "atan"::SY) => ataneval(f, lk, k, v)
+ is?(k, 'log) => logeval(f, lk, k, v)
+ is?(k, 'exp) => expeval(f, lk, k, v)
+ is?(k, 'tan) => taneval(f, lk, k, v)
+ is?(k, 'atan) => ataneval(f, lk, k, v)
is?(k, NTHR) => rooteval(f, lk, k, v(minIndex v))
[f, empty(), empty()]
@@ -358,7 +358,7 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
u := first argument k
fns := toU lk
c := u - +/[qelt(v, i) * x for i in minIndex v .. maxIndex v for x in fns]
- (rec := goodCoef(v, lk, "tan"::SY)) case "failed" =>
+ (rec := goodCoef(v, lk, 'tan)) case "failed" =>
tannosimp(f, lk, k, v, fns, c)
v0 := retract(inv qelt(v, rec.index))@Z
lv := [qelt(v, i) for i in minIndex v .. maxIndex v |
@@ -369,7 +369,7 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
[eval(f, [rec.ker], [g]), [rec.ker], [g]]
tannosimp(f, lk, k, v, fns, c) ==
- every?(is?(#1, "tan"::SY), lk) =>
+ every?(is?(#1, 'tan), lk) =>
dd := (d := (cd := splitDenominator v).den)::F
newt := [tan(u / dd) for u in fns]$List(F)
newtan := [tanNa(t, d) for t in newt]$List(F)
@@ -383,7 +383,7 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
[eval(f, [k], [h]), [k], [h]]
expnosimp(f, lk, k, v, fns, g) ==
- every?(is?(#1, "exp"::SY), lk) =>
+ every?(is?(#1, 'exp), lk) =>
dd := (d := (cd := splitDenominator v).den)::F
newe := [exp(y / dd) for y in fns]$List(F)
newexp := [e ** d for e in newe]$List(F)
@@ -463,7 +463,7 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where
y := first argument k
fns := toY lk
g := y - +/[qelt(v, i) * z for i in minIndex v .. maxIndex v for z in fns]
- (rec := goodCoef(v, lk, "exp"::SY)) case "failed" =>
+ (rec := goodCoef(v, lk, 'exp)) case "failed" =>
expnosimp(f, lk, k, v, fns, exp g)
v0 := retract(inv qelt(v, rec.index))@Z
lv := [qelt(v, i) for i in minIndex v .. maxIndex v |
@@ -520,7 +520,6 @@ InnerTrigonometricManipulations(R,F,FG): Exports == Implementation where
KG ==> Kernel FG
PG ==> SparseMultivariatePolynomial(GR, KG)
UP ==> SparseUnivariatePolynomial PG
- NTHR ==> "nthRoot"::SY
Exports ==> with
GF2FG : GF -> FG
@@ -543,6 +542,7 @@ InnerTrigonometricManipulations(R,F,FG): Exports == Implementation where
++ \spad{exp(2*u)} otherwise.
Implementation ==> add
+ macro NTHR == 'nthRoot
ker2explogs: (KG, List KG, List SY) -> FG
smp2explogs: (PG, List KG, List SY) -> FG
supexp : (UP, GF, GF, Z) -> GF
@@ -744,12 +744,12 @@ TrigonometricManipulations(R, F): Exports == Implementation where
-- "failed" otherwise
kcomplex k ==
op := operator k
- is?(k, "nthRoot"::SY) =>
+ is?(k, 'nthRoot) =>
arg := argument k
even?(retract(n := second arg)@Z) and ((u := sign(first arg)) case Z)
and (u::Z < 0) => op(s1, n / 2::F) * op(- first arg, n)
"failed"
- is?(k, "log"::SY) and ((u := sign(a := first argument k)) case Z)
+ is?(k, 'log) and ((u := sign(a := first argument k)) case Z)
and (u::Z < 0) => op(- a) + ipi
"failed"
@@ -796,7 +796,7 @@ TrigonometricManipulations(R, F): Exports == Implementation where
localexplogs(f, g, lx) ==
trigs2explogs(F2FG g, [K2KG k for k in tower f
- | is?(k, "tan"::SY) or is?(k, "cot"::SY)], lx)
+ | is?(k, 'tan) or is?(k, 'cot)], lx)
trigs f ==
real? f => f
@@ -877,7 +877,7 @@ ComplexTrigonometricManipulations(R, F): Exports == Implementation where
localexplogs(f, g, lx) ==
trigs2explogs(g, [k for k in tower f
- | is?(k, "tan"::SY) or is?(k, "cot"::SY)], lx)
+ | is?(k, 'tan) or is?(k, 'cot)], lx)
complexElementary f ==
any?(has?(#1, 'rtrig),
diff --git a/src/algebra/exprode.spad.pamphlet b/src/algebra/exprode.spad.pamphlet
index 2693eabf..8a9bf6d4 100644
--- a/src/algebra/exprode.spad.pamphlet
+++ b/src/algebra/exprode.spad.pamphlet
@@ -155,7 +155,7 @@ ExpressionSpaceODESolver(R, F): Exports == Implementation where
checkSystem(diffeq, yx, lv) ==
for k in kernels diffeq repeat
- is?(k, "%diff"::SY) =>
+ is?(k, '%diff) =>
return div2exquo subst(diffRhsK(k, diffeq), yx, lv)
0
diff --git a/src/algebra/fspace.spad.pamphlet b/src/algebra/fspace.spad.pamphlet
index 91e565d3..6196c550 100644
--- a/src/algebra/fspace.spad.pamphlet
+++ b/src/algebra/fspace.spad.pamphlet
@@ -24,9 +24,6 @@ ExpressionSpace(): Category == Defn where
K ==> Kernel %
OP ==> BasicOperator
SY ==> Symbol
- PAREN ==> "%paren"::SY
- BOX ==> "%box"::SY
- DUMMYVAR ==> "%dummyVar"
Defn ==> Join(OrderedSet, RetractableTo K,
InnerEvalable(K, %), Evalable %) with
@@ -168,6 +165,9 @@ ExpressionSpace(): Category == Defn where
-- subst:(%, List K, List %) -> %
-- eval:(%, List Symbol, List(List % -> %)) -> %
+ macro PAREN == '%paren
+ macro BOX == '%box
+ macro DUMMYVAR == '%dummyVar
allKernels: % -> Set K
listk : % -> List K
allk : List % -> Set K
@@ -287,7 +287,7 @@ ExpressionSpace(): Category == Defn where
distribute(x, y) ==
ky := retract y
unwrap([k for k in listk x |
- is?(k, "%paren"::SY) and member?(ky, listk(k::%))], x)
+ is?(k, '%paren) and member?(ky, listk(k::%))], x)
-- in case of conflicting substitutions e.g. [x = a, x = b],
-- the first one prevails.
@@ -556,8 +556,8 @@ FunctionSpace(R:OrderedSet): Category == Definition where
equaldiff : (K,K)->Boolean
debugA: (List % ,List %,Boolean) -> Boolean
- opdiff := operator("%diff"::SY)$CommonOperators()
- opquote := operator("applyQuote"::SY)$CommonOperators
+ opdiff := operator('%diff)$CommonOperators()
+ opquote := operator('applyQuote)$CommonOperators
ground? x == retractIfCan(x)@Union(R,"failed") case R
ground x == retract x
@@ -572,8 +572,8 @@ FunctionSpace(R:OrderedSet): Category == Definition where
subs(fn, k) == kernel(operator k,[fn x for x in argument k]$List(%))
operator op ==
- is?(op, "%diff"::SY) => opdiff
- is?(op, "%quote"::SY) => opquote
+ is?(op, '%diff) => opdiff
+ is?(op, '%quote) => opquote
error "Unknown operator"
if R has ConvertibleTo InputForm then
diff --git a/src/algebra/intaf.spad.pamphlet b/src/algebra/intaf.spad.pamphlet
index 83ba77fb..d226fa79 100644
--- a/src/algebra/intaf.spad.pamphlet
+++ b/src/algebra/intaf.spad.pamphlet
@@ -600,8 +600,8 @@ PureAlgebraicIntegration(R, F, L): Exports == Implementation where
palgint(f, x, y) ==
(v := linearInXIfCan(x, y)) case "failed" =>
(u := quadIfCan(x, y)) case "failed" =>
- is?(y, "nthRoot"::SY) => prootintegrate(f, x, y)
- is?(y, "rootOf"::SY) => palgintegrate(f, x, y)
+ is?(y, 'nthRoot) => prootintegrate(f, x, y)
+ is?(y, 'rootOf) => palgintegrate(f, x, y)
FAIL
palgint0(f, x, y, u.coef, u.poly)
palgint0(f, x, y, dumk, v.xsub, v.dxsub)
@@ -609,8 +609,8 @@ PureAlgebraicIntegration(R, F, L): Exports == Implementation where
palgextint(f, x, y, g) ==
(v := linearInXIfCan(x, y)) case "failed" =>
(u := quadIfCan(x, y)) case "failed" =>
- is?(y, "nthRoot"::SY) => prootextint(f, x, y, g)
- is?(y, "rootOf"::SY) => palgext(f, x, y, g)
+ is?(y, 'nthRoot) => prootextint(f, x, y, g)
+ is?(y, 'rootOf) => palgext(f, x, y, g)
FAIL
palgextint0(f, x, y, g, u.coef, u.poly)
palgextint0(f, x, y, g, dumk, v.xsub, v.dxsub)
@@ -618,8 +618,8 @@ PureAlgebraicIntegration(R, F, L): Exports == Implementation where
palglimint(f, x, y, lu) ==
(v := linearInXIfCan(x, y)) case "failed" =>
(u := quadIfCan(x, y)) case "failed" =>
- is?(y, "nthRoot"::SY) => prootlimint(f, x, y, lu)
- is?(y, "rootOf"::SY) => palglim(f, x, y, lu)
+ is?(y, 'nthRoot) => prootlimint(f, x, y, lu)
+ is?(y, 'rootOf) => palglim(f, x, y, lu)
FAIL
palglimint0(f, x, y, lu, u.coef, u.poly)
palglimint0(f, x, y, lu, dumk, v.xsub, v.dxsub)
@@ -627,7 +627,7 @@ PureAlgebraicIntegration(R, F, L): Exports == Implementation where
palgRDE(nfp, f, g, x, y, rde) ==
(v := linearInXIfCan(x, y)) case "failed" =>
(u := quadIfCan(x, y)) case "failed" =>
- is?(y, "nthRoot"::SY) => prootRDE(nfp, f, g, x, y, rde)
+ is?(y, 'nthRoot) => prootRDE(nfp, f, g, x, y, rde)
palgRDE1(nfp, g, x, y)
palgRDE0(f, g, x, y, rde, u.coef, u.poly)
palgRDE0(f, g, x, y, rde, dumk, v.xsub, v.dxsub)
@@ -722,8 +722,8 @@ AlgebraicIntegration(R, F): Exports == Implementation where
(multivariate(cf, t) * k::F)
algint(f, t, y, derivation) ==
- is?(y, "nthRoot"::SY) => rootintegrate(f, t, y, derivation)
- is?(y, "rootOf"::SY) => algintegrate(f, t, y, derivation)
+ is?(y, 'nthRoot) => rootintegrate(f, t, y, derivation)
+ is?(y, 'rootOf) => algintegrate(f, t, y, derivation)
FAIL
@
diff --git a/src/algebra/intef.spad.pamphlet b/src/algebra/intef.spad.pamphlet
index 7e96e6f2..ab6821ba 100644
--- a/src/algebra/intef.spad.pamphlet
+++ b/src/algebra/intef.spad.pamphlet
@@ -99,7 +99,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
tryChangeVar: (F, K, SE) -> Union(IR, "failed")
droponex : (F, F, K, F) -> Union(F, "failed")
- prim?(k, x) == is?(k, "log"::SE) or has?(operator k, 'prim)
+ prim?(k, x) == is?(k, 'log) or has?(operator k, 'prim)
tanint(f, x, k) ==
eta' := differentiate(eta := first argument k, x)
@@ -147,7 +147,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
alglfint(f, k, l, x) ==
xf := x::F
symbolIfCan(kx := ksec(k,l,x)) case SE => addx(palgint(f, kx, k), xf)
- is?(kx, "exp"::SE) => addx(algexpint(f, kx, k, x), xf)
+ is?(kx, 'exp) => addx(algexpint(f, kx, k, x), xf)
prim?(kx, x) => addx(algprimint(f, kx, k, x), xf)
has?(operator kx, ALGOP) =>
rec := primitiveElement(kx::F, k::F)
@@ -167,7 +167,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
ky := retract(y)@K
r := u::Record(ratpart:F, coeff:F)
[eval(r.ratpart,ky,rec.primelt), eval(r.coeff,ky,rec.primelt)]
- is?(kx, "exp"::SE) or is?(kx, "log"::SE) => FAIL
+ is?(kx, 'exp) or is?(kx, 'log) => FAIL
unkextint(f, x, g)
alglflimint(f, k, l, x, lu) ==
@@ -183,7 +183,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
[eval(r.mainpart, ky, rec.primelt),
[[eval(rc.coeff, ky, rec.primelt),
eval(rc.logand,ky, rec.primelt)] for rc in r.limitedlogs]]
- is?(kx, "exp"::SE) or is?(kx, "log"::SE) => FAIL
+ is?(kx, 'exp) or is?(kx, 'log) => FAIL
unklimint(f, x, lu)
if R has Join(ConvertibleTo Pattern Integer, PatternMatchable Integer)
@@ -199,8 +199,8 @@ ElementaryIntegration(R, F): Exports == Implementation where
empty?(l := varselect(kernels f, x)) => (xf * f)::IR
symbolIfCan(k := kmax l) case SE =>
map(multivariate(#1, k), integrate univariate(f, k))
- is?(k, "tan"::SE) => addx(tanint(f, x, k), xf)
- is?(k, "exp"::SE) => addx(expint(f, x, k), xf)
+ is?(k, 'tan) => addx(tanint(f, x, k), xf)
+ is?(k, 'exp) => addx(expint(f, x, k), xf)
prim?(k, x) => addx(primint(f, x, k), xf)
has?(operator k, ALGOP) => alglfint(f, k, l, x)
unknownint(f, x)
@@ -233,7 +233,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
case SE =>
map(multivariate(#1, k), extendedint(univariate(f, k),
univariate(g, k)))
- is?(k, "exp"::SE) => expextint(f, x, k, g)
+ is?(k, 'exp) => expextint(f, x, k, g)
prim?(k, x) => primextint(f, x, k, g)
has?(operator k, ALGOP) => alglfextint(f, k, l, x, g)
unkextint(f, x, g)
@@ -243,7 +243,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
symbolIfCan(k := kmax(l)) case SE =>
map(multivariate(#1, k), limitedint(univariate(f, k),
[univariate(u, k) for u in lu]))
- is?(k, "exp"::SE) => explimint(f, x, k, lu)
+ is?(k, 'exp) => explimint(f, x, k, lu)
prim?(k, x) => primlimint(f, x, k, lu)
has?(operator k, ALGOP) => alglflimint(f, k, l, x, lu)
unklimint(f, x, lu)
@@ -254,7 +254,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
primextint(f, x, k, g) ==
lk := varselect([a for a in tower f
- | k ~= a and is?(a, "log"::SE)], x)
+ | k ~= a and is?(a, 'log)], x)
(u1 := primextendedint(univariate(f, k), differentiate(#1,
differentiate(#1, x), differentiate(k::F, x)::UP),
lfextlimint(#1, x, k, lk), univariate(g, k))) case "failed"
@@ -278,7 +278,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
primint(f, x, k) ==
lk := varselect([a for a in tower f
- | k ~= a and is?(a, "log"::SE)], x)
+ | k ~= a and is?(a, 'log)], x)
r1 := primintegrate(univariate(f, k), differentiate(#1,
differentiate(#1, x), differentiate(k::F, x)::UP),
lfextlimint(#1, x, k, lk))
@@ -289,7 +289,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
case "failed") => u1
twr := tower f
empty?(lg := [kk for kk in lk | not member?(kk, twr)]) => "failed"
- is?(k, "log"::SE) =>
+ is?(k, 'log) =>
(u2 := lflimitedint(f, x,
[first argument u for u in union(lg, [k])])) case "failed"
=> "failed"
@@ -313,7 +313,7 @@ ElementaryIntegration(R, F): Exports == Implementation where
primlimint(f, x, k, lu) ==
lk := varselect([a for a in tower f
- | k ~= a and is?(a, "log"::SE)], x)
+ | k ~= a and is?(a, 'log)], x)
(u1 := primlimitedint(univariate(f, k), differentiate(#1,
differentiate(#1, x), differentiate(k::F, x)::UP),
lfextlimint(#1, x, k, lk), [univariate(u, k) for u in lu]))
diff --git a/src/algebra/integrat.spad.pamphlet b/src/algebra/integrat.spad.pamphlet
index 9fce6205..fb83e7f3 100644
--- a/src/algebra/integrat.spad.pamphlet
+++ b/src/algebra/integrat.spad.pamphlet
@@ -76,7 +76,7 @@ FunctionSpaceComplexIntegration(R, F): Exports == Implementation where
[k for k in tower(g := realElementary(f, x))
| member?(x, variables(k::F))]$List(Kernel F))$List(Kernel F) =>
h := trigs2explogs(F2FG g, [K2KG k for k in tower f
- | is?(k, "tan"::SE) or is?(k, "cot"::SE)], [x])
+ | is?(k, 'tan) or is?(k, 'cot)], [x])
real?(g := FG2F h) =>
internalIntegrate0(rootSimp(rischNormalize(g, x).func), x)
real?(g := FG2F(h := rootSimp(rischNormalize(h, x).func))) =>
@@ -149,7 +149,7 @@ FunctionSpaceIntegration(R, F): Exports == Implementation where
tan2temp k == kernel(optemp, argument k, height k)$K
trans? f ==
- any?(is?(#1,"log"::SE) or is?(#1,"exp"::SE) or is?(#1,"atan"::SE),
+ any?(is?(#1,'log) or is?(#1,'exp) or is?(#1,'atan),
operators f)$List(BasicOperator)
mkPrimh(f, x, h, comp) ==
@@ -198,19 +198,19 @@ FunctionSpaceIntegration(R, F): Exports == Implementation where
R has complex or not real? f => complexIntegrate(f, x)
f := distribute(f, x::F)
tf := [k for k in tower f | member?(x, variables(k::F)@List(SE))]$List(K)
- ltf := select(is?(operator #1, "tan"::SE), tf)
+ ltf := select(is?(operator #1, 'tan), tf)
ht := any?(has?(operator #1, 'htrig), tf)
rec := rischNormalize(realElementary(f, x), x)
g := rootSimp(rec.func)
tg := [k for k in tower g | member?(x, variables(k::F))]$List(K)
- ltg := select(is?(operator #1, "tan"::SE), tg)
+ ltg := select(is?(operator #1, 'tan), tg)
rtg := any?(has?(operator #1, 'rtrig), tg)
el := any?(has?(operator #1, 'elem), tg)
i:IR
if (comp := goComplex?(rtg, tg, ltg)) then
i := map(FG2F, lfintegrate(trigs2explogs(F2FG g,
- [K2KG k for k in tf | is?(k, "tan"::SE) or
- is?(k, "cot"::SE)], [x]), x))
+ [K2KG k for k in tf | is?(k, 'tan) or
+ is?(k, 'cot)], [x]), x))
else i := lfintegrate(g, x)
ltg := setDifference(ltg, ltf) -- tan's added by normalization
(u := rinteg(i, f, x, el and ht, comp)) case F =>
diff --git a/src/algebra/intpm.spad.pamphlet b/src/algebra/intpm.spad.pamphlet
index 3fb0f60a..aca1a275 100644
--- a/src/algebra/intpm.spad.pamphlet
+++ b/src/algebra/intpm.spad.pamphlet
@@ -138,10 +138,10 @@ PatternMatchIntegration(R, F): Exports == Implementation where
goodlilog? : (K, P) -> Boolean
gooddilog? : (K, P, P) -> Boolean
- goodlilog?(k, p) == is?(k, "log"::SY) and one? minimumDegree(p, k)
+ goodlilog?(k, p) == is?(k, 'log) and one? minimumDegree(p, k)
gooddilog?(k, p, q) ==
- is?(k, "log"::SY) and one? degree(p, k) and zero? degree(q, k)
+ is?(k, 'log) and one? degree(p, k) and zero? degree(q, k)
-- matches the integral to a result of the form d * erf(u) or d * ei(u)
-- returns [case, u, d]
diff --git a/src/algebra/laplace.spad.pamphlet b/src/algebra/laplace.spad.pamphlet
index 9652f91d..28e2a1dd 100644
--- a/src/algebra/laplace.spad.pamphlet
+++ b/src/algebra/laplace.spad.pamphlet
@@ -116,7 +116,7 @@ LaplaceTransform(R, F): Exports == Implementation where
-- returns [a, c, b] iff f = a * exp(c * t + b)
-- and b and c do not involve t
aexp(f, t) ==
- is?(f, "exp"::SE) =>
+ is?(f, 'exp) =>
(v := isLinear(first argument(retract(f)@K),t)) case "failed" =>
"failed"
[1, v.nconst, v.const]
@@ -162,7 +162,7 @@ LaplaceTransform(R, F): Exports == Implementation where
lapkernel(f, t, tt, ss) ==
(k := retractIfCan(f)@Union(K, "failed")) case "failed" => "failed"
empty?(arg := argument(k::K)) => "failed"
- is?(op := operator k, "%diff"::SE) =>
+ is?(op := operator k, '%diff) =>
not( #arg = 3) => "failed"
not(is?(arg.3, t)) => "failed"
fint := eval(arg.1, arg.2, tt)
@@ -170,11 +170,11 @@ LaplaceTransform(R, F): Exports == Implementation where
ss * locallaplace(fint, t, tt, s, ss) - eval(fint, tt = 0)
not (empty?(rest arg)) => "failed"
member?(t, variables(a := first(arg) / tt)) => "failed"
- is?(op := operator k, "Si"::SE) => atan(a / ss) / ss
- is?(op, "Ci"::SE) => log((ss**2 + a**2) / a**2) / (2 * ss)
- is?(op, "Ei"::SE) => log((ss + a) / a) / ss
+ is?(op := operator k, 'Si) => atan(a / ss) / ss
+ is?(op, 'Ci) => log((ss**2 + a**2) / a**2) / (2 * ss)
+ is?(op, 'Ei) => log((ss + a) / a) / ss
if F has SpecialFunctionCategory then
- is?(op, "log"::SE) => (digamma(1) - log(a) - log(ss)) / ss
+ is?(op, 'log) => (digamma(1) - log(a) - log(ss)) / ss
"failed"
-- Below we try to apply one of the texbook rules for computing
diff --git a/src/algebra/limitps.spad.pamphlet b/src/algebra/limitps.spad.pamphlet
index 2ae98c68..b2f66076 100644
--- a/src/algebra/limitps.spad.pamphlet
+++ b/src/algebra/limitps.spad.pamphlet
@@ -701,8 +701,8 @@ ElementaryFunctionSign(R,F): Exports == Implementation where
kerSign k ==
has?(op := operator k, NEGAT) => -1
- has?(op, POSIT) or is?(op, "pi"::SY) or is?(op,"exp"::SY) or
- is?(op,"cosh"::SY) or is?(op,"sech"::SY) => 1
+ has?(op, POSIT) or is?(op, 'pi) or is?(op,'exp) or
+ is?(op,'cosh) or is?(op,'sech) => 1
empty?(arg := argument k) => "failed"
(s := sign first arg) case "failed" =>
is?(op,"nthRoot" :: SY) =>
diff --git a/src/algebra/liouv.spad.pamphlet b/src/algebra/liouv.spad.pamphlet
index 7f730bfd..587f8b23 100644
--- a/src/algebra/liouv.spad.pamphlet
+++ b/src/algebra/liouv.spad.pamphlet
@@ -104,7 +104,7 @@ LiouvillianFunction(R, F): Exports == Implementation where
kernel(opint, l)
ddint l ==
- int(integrand(l)::O * hconcat("d"::SE::O, third(l)::O),
+ int(integrand(l)::O * hconcat('d::O, third(l)::O),
third(rest l)::O, third(rest rest l)::O)
eqint(k1,k2) ==
@@ -178,7 +178,7 @@ LiouvillianFunction(R, F): Exports == Implementation where
pint : List INP -> INP
- pint l == convert concat(convert("integral"::SE)@INP, l)
+ pint l == convert concat(convert('integral)@INP, l)
inint l ==
r2:= convert([convert("::"::SE)@INP,convert(third l)@INP,convert("Symbol"::SE)@INP]@List INP)@INP
pint [convert(integrand l)@INP, r2]
diff --git a/src/algebra/odeef.spad.pamphlet b/src/algebra/odeef.spad.pamphlet
index ed29a09c..8f71bbc0 100644
--- a/src/algebra/odeef.spad.pamphlet
+++ b/src/algebra/odeef.spad.pamphlet
@@ -360,7 +360,6 @@ ElementaryFunctionODESolver(R, F): Exports == Implementation where
SYS ==> Record(mat:M, vec: V)
U ==> Union(REC, F, "failed")
UU ==> Union(F, "failed")
- OPDIFF ==> "%diff"::SY
Exports ==> with
solve: (M, V, SY) -> Union(VEC, "failed")
@@ -426,6 +425,7 @@ ElementaryFunctionODESolver(R, F): Exports == Implementation where
++ \spad{dy/dx = f(x,y)};
Implementation ==> add
+ macro OPDIFF == '%diff
import ODEIntegration(R, F)
import IntegrationTools(R, F)
import NonLinearFirstOrderODESolver(R, F)
diff --git a/src/algebra/oderf.spad.pamphlet b/src/algebra/oderf.spad.pamphlet
index 96e1f9f1..08ba4213 100644
--- a/src/algebra/oderf.spad.pamphlet
+++ b/src/algebra/oderf.spad.pamphlet
@@ -751,10 +751,10 @@ ODEIntegration(R, F): Exports == Implementation where
-- checks if a non-sum expr is of the form c * log(g) for a rational number c
isQlog f ==
- is?(f, "log"::SY) => [1, first argument(retract(f)@K)]
+ is?(f, 'log) => [1, first argument(retract(f)@K)]
(v := isTimes f) case List(F) and (#(l := v::List(F)) <= 3) =>
l := reverse_! sort_! l
- is?(first l, "log"::SY) and ((u := isQ rest l) case Q) =>
+ is?(first l, 'log) and ((u := isQ rest l) case Q) =>
[u::Q, first argument(retract(first(l))@K)]
"failed"
"failed"
diff --git a/src/algebra/rdeef.spad.pamphlet b/src/algebra/rdeef.spad.pamphlet
index 787393b1..0f5c1ffb 100644
--- a/src/algebra/rdeef.spad.pamphlet
+++ b/src/algebra/rdeef.spad.pamphlet
@@ -76,7 +76,7 @@ IntegrationTools(R:OrderedSet, F:FunctionSpace R): Exp == Impl where
better?(x, y) ==
height(y) ~= height(x) => height(y) < height(x)
has?(operator y, ALGOP) or
- (is?(y, "exp"::SE) and not is?(x, "exp"::SE)
+ (is?(y,'exp) and not is?(x, 'exp)
and not has?(operator x, ALGOP))
if R has IntegralDomain then
@@ -108,7 +108,7 @@ IntegrationTools(R:OrderedSet, F:FunctionSpace R): Exp == Impl where
cont(unitNormal(leadingCoefficient q).unit * content q, rest l)
linearLog?(k, f, x) ==
- is?(k, "log"::SE) and
+ is?(k, 'log) and
((u := retractIfCan(univariate(f,k))@Union(UP,"failed")) case UP)
and one?(degree(u::UP))
and not member?(x, variables leadingCoefficient(u::UP))
@@ -226,7 +226,7 @@ ElementaryRischDE(R, F): Exports == Implementation where
RF2GP f == (numer(f)::GP exquo denom(f)::GP)::GP
logdiff(twr, bad) ==
- [u for u in twr | is?(u, "log"::SE) and not member?(u, bad)]
+ [u for u in twr | is?(u, 'log) and not member?(u, bad)]
rischDEalg(n, nfp, f, g, k, l, x, limint, extint) ==
symbolIfCan(kx := ksec(k, l, x)) case SE =>
@@ -252,7 +252,7 @@ ElementaryRischDE(R, F): Exports == Implementation where
freeOf?(y := g / nfp, x) => [y, g, true]
vl := varselect(union(kernels nfp, kernels g), x)
symbolIfCan(k := kmax vl) case SE => normalise0(n, f, g, x)
- is?(k, "log"::SE) or is?(k, "exp"::SE) =>
+ is?(k, 'log) or is?(k, 'exp) =>
normalise(n, nfp, f, g, x, k, limitedint, extendedint)
has?(operator k, ALGOP) =>
rischDEalg(n, nfp, f, g, k, vl, x, limitedint, extendedint)
@@ -294,12 +294,12 @@ ElementaryRischDE(R, F): Exports == Implementation where
newg := univariate(p::F * g, k)
twr := union(logdiff(tower f, empty()), logdiff(tower g, empty()))
ans1 :=
- is?(k, "log"::SE) =>
+ is?(k, 'log) =>
rischDElog(twr, newf, newg, x, k,
differentiate(#1, differentiate(#1, x),
differentiate(k::F, x)::UP),
limitedint, extendedint)
- is?(k, "exp"::SE) =>
+ is?(k, 'exp) =>
rischDEexp(twr, newf, newg, x, k,
differentiate(#1, differentiate(#1, x),
monomial(differentiate(first argument k, x), 1)),
@@ -312,7 +312,7 @@ ElementaryRischDE(R, F): Exports == Implementation where
disasters := empty()$Data
fnum := numer f
fden := denom f
- for u in varselect(kernels f, x) | is?(u, "log"::SE) repeat
+ for u in varselect(kernels f, x) | is?(u, 'log) repeat
logand := first argument u
if zero?(degree univariate(fden, u)) and
one?(degree(num := univariate(fnum, u))) then
diff --git a/src/algebra/strap/SYMBOL.lsp b/src/algebra/strap/SYMBOL.lsp
index c216ea58..6e61215a 100644
--- a/src/algebra/strap/SYMBOL.lsp
+++ b/src/algebra/strap/SYMBOL.lsp
@@ -113,6 +113,8 @@
(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Thing|) |SYMBOL;sample;$;35|))
+(PUT '|SYMBOL;sample;$;35| '|SPADreplace| '(XLAM NIL '|aSymbol|))
+
(DEFUN |SYMBOL;writeOMSym| (|dev| |x| $)
(COND
((|SYMBOL;scripted?;$B;30| |x| $)
@@ -752,7 +754,7 @@
(|error| "Cannot convert a symbol to a list if it is not subscripted"))
('T |sy|)))
-(DEFUN |SYMBOL;sample;$;35| ($) (|SYMBOL;coerce;S$;8| "aSymbol" $))
+(DEFUN |SYMBOL;sample;$;35| ($) (DECLARE (IGNORE $)) '|aSymbol|)
(DEFUN |Symbol| ()
(PROG ()
diff --git a/src/algebra/symbol.spad.pamphlet b/src/algebra/symbol.spad.pamphlet
index b41a4f0a..6287037b 100644
--- a/src/algebra/symbol.spad.pamphlet
+++ b/src/algebra/symbol.spad.pamphlet
@@ -314,7 +314,7 @@ Symbol(): Exports == Implementation where
error "Cannot convert a symbol to a list if it is not subscripted"
sy pretend List(%)
- sample() == "aSymbol"::%
+ sample() == 'aSymbol
@
diff --git a/src/algebra/transsolve.spad.pamphlet b/src/algebra/transsolve.spad.pamphlet
index d3c23777..f4bb6f6b 100644
--- a/src/algebra/transsolve.spad.pamphlet
+++ b/src/algebra/transsolve.spad.pamphlet
@@ -283,7 +283,7 @@ TransSolvePackage(R) : Exports == Implementation where
while testRootk(var1,y) repeat
varlistk1:=tableXkernels(var1,y)
for i in varlistk1 repeat
- if is?(i, "nthRoot"::S) then
+ if is?(i, 'nthRoot) then
var1:=eliminateKernRoot(var1,first kernels(i::RE))
var1
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-23 09:01:51 +0000