diff options
Diffstat (limited to 'src/algebra/elemntry.spad.pamphlet')
| -rw-r--r-- | src/algebra/elemntry.spad.pamphlet | 42 |
1 files changed, 14 insertions, 28 deletions
diff --git a/src/algebra/elemntry.spad.pamphlet b/src/algebra/elemntry.spad.pamphlet index 9a9bdeb2..356bf647 100644 --- a/src/algebra/elemntry.spad.pamphlet +++ b/src/algebra/elemntry.spad.pamphlet @@ -326,24 +326,20 @@ ElementaryFunction(R, F): Exports == Implementation where even?(n::Z) => valueOrPole(values.m) valueOrPole(values.(m+1)) (n := retractIfCan(2*q)@Union(Z, "failed")) case Z => --- one?(s := posrem(n::Z, 4)) => valueOrPole(values.(m+2)) - (s := posrem(n::Z, 4)) = 1 => valueOrPole(values.(m+2)) + one?(s := posrem(n::Z, 4)) => valueOrPole(values.(m+2)) valueOrPole(values.(m+3)) (n := retractIfCan(3*q)@Union(Z, "failed")) case Z => --- one?(s := posrem(n::Z, 6)) => valueOrPole(values.(m+4)) - (s := posrem(n::Z, 6)) = 1 => valueOrPole(values.(m+4)) + one?(s := posrem(n::Z, 6)) => valueOrPole(values.(m+4)) s = 2 => valueOrPole(values.(m+5)) s = 4 => valueOrPole(values.(m+6)) valueOrPole(values.(m+7)) (n := retractIfCan(4*q)@Union(Z, "failed")) case Z => --- one?(s := posrem(n::Z, 8)) => valueOrPole(values.(m+8)) - (s := posrem(n::Z, 8)) = 1 => valueOrPole(values.(m+8)) + one?(s := posrem(n::Z, 8)) => valueOrPole(values.(m+8)) s = 3 => valueOrPole(values.(m+9)) s = 5 => valueOrPole(values.(m+10)) valueOrPole(values.(m+11)) (n := retractIfCan(6*q)@Union(Z, "failed")) case Z => --- one?(s := posrem(n::Z, 12)) => valueOrPole(values.(m+12)) - (s := posrem(n::Z, 12)) = 1 => valueOrPole(values.(m+12)) + one?(s := posrem(n::Z, 12)) => valueOrPole(values.(m+12)) s = 5 => valueOrPole(values.(m+13)) s = 7 => valueOrPole(values.(m+14)) valueOrPole(values.(m+15)) @@ -463,8 +459,7 @@ ElementaryFunction(R, F): Exports == Implementation where iasin x == zero? x => 0 --- one? x => pi() / (2::F) - (x = 1) => pi() / (2::F) + one? x => pi() / (2::F) x = -1 => - pi() / (2::F) y := dropfun x is?(x, opsin) => y @@ -473,8 +468,7 @@ ElementaryFunction(R, F): Exports == Implementation where iacos x == zero? x => pi() / (2::F) --- one? x => 0 - (x = 1) => 0 + one? x => 0 x = -1 => pi() y := dropfun x is?(x, opsin) => pi() / (2::F) - y @@ -483,12 +477,10 @@ ElementaryFunction(R, F): Exports == Implementation where iatan x == zero? x => 0 --- one? x => pi() / (4::F) - (x = 1) => pi() / (4::F) + one? x => pi() / (4::F) x = -1 => - pi() / (4::F) x = (r3:=iisqrt3()) => pi() / (3::F) --- one?(x*r3) => pi() / (6::F) - (x*r3) = 1 => pi() / (6::F) + one?(x*r3) => pi() / (6::F) y := dropfun x is?(x, optan) => y is?(x, opcot) => pi() / (2::F) - y @@ -496,13 +488,11 @@ ElementaryFunction(R, F): Exports == Implementation where iacot x == zero? x => pi() / (2::F) --- one? x => pi() / (4::F) - (x = 1) => pi() / (4::F) + one? x => pi() / (4::F) x = -1 => 3 * pi() / (4::F) x = (r3:=iisqrt3()) => pi() / (6::F) x = -r3 => 5 * pi() / (6::F) --- one?(xx:=x*r3) => pi() / (3::F) - (xx:=x*r3) = 1 => pi() / (3::F) + one?(xx:=x*r3) => pi() / (3::F) xx = -1 => 2* pi() / (3::F) y := dropfun x is?(x, optan) => pi() / (2::F) - y @@ -511,8 +501,7 @@ ElementaryFunction(R, F): Exports == Implementation where iasec x == zero? x => INV --- one? x => 0 - (x = 1) => 0 + one? x => 0 x = -1 => pi() y := dropfun x is?(x, opsec) => y @@ -521,8 +510,7 @@ ElementaryFunction(R, F): Exports == Implementation where iacsc x == zero? x => INV --- one? x => pi() / (2::F) - (x = 1) => pi() / (2::F) + one? x => pi() / (2::F) x = -1 => - pi() / (2::F) y := dropfun x is?(x, opsec) => pi() / (2::F) - y @@ -650,8 +638,7 @@ ElementaryFunction(R, F): Exports == Implementation where iiilog x == zero? x => INV --- one? x => 0 - (x = 1) => 0 + one? x => 0 (u := isExpt(x, opexp)) case Record(var:K, exponent:Integer) => rec := u::Record(var:K, exponent:Integer) arg := first argument(rec.var); @@ -660,8 +647,7 @@ ElementaryFunction(R, F): Exports == Implementation where ilog x ilog x == --- ((num1 := one?(num := numer x)) or num = -1) and (den := denom x) ~= 1 - ((num1 := ((num := numer x) = 1)) or num = -1) and (den := denom x) ~= 1 + ((num1 := one?(num := numer x)) or num = -1) and (den := denom x) ~= 1 and empty? variables x => - kernel(oplog, (num1 => den; -den)::F) kernel(oplog, x) |