diff options
Diffstat (limited to 'src/algebra/riccati.spad.pamphlet')
| -rw-r--r-- | src/algebra/riccati.spad.pamphlet | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/src/algebra/riccati.spad.pamphlet b/src/algebra/riccati.spad.pamphlet index 43a3c5f1..0fdbe47c 100644 --- a/src/algebra/riccati.spad.pamphlet +++ b/src/algebra/riccati.spad.pamphlet @@ -113,7 +113,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where dmax(rec, c, l) == innermax(rec, l, - order(#1, c)::Z) tau0(p, q) == ((q exquo (p ** order(q, p)))::UP) rem p poly1(c, cp, i) == */[monomial(1,1)$UP2 - (j * cp)::UP2 for j in 0..i-1] - getIndices(n, l) == removeDuplicates_! concat [r.ij for r in l | r.deg=n] + getIndices(n, l) == removeDuplicates! concat [r.ij for r in l | r.deg=n] denomRicDE l == */[c ** bound(c, l) for c in factoredDenomRicDE l] polyRicDE(l, zeros) == concat([0, l], polysol(l, 0, false, zeros)) @@ -126,7 +126,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where ans:List(FRC) := empty() finite? and zero? b => ans lc := leadingDenomRicDE(c, op) - if finite? then lc := select_!(#1.deg <= b, lc) + if finite? then lc := select!(#1.deg <= b, lc) for rec in lc repeat for r in zeros(c, rec.eq) | r ~= 0 repeat rcn := r /$RF (c ** rec.deg) @@ -134,7 +134,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where sols := padicsol(c, neweq, (rec.deg-1)::N, true, zeros) ans := empty? sols => concat([rcn, neweq], ans) - concat_!([[rcn + sol.frac, sol.eq] for sol in sols], ans) + concat!([[rcn + sol.frac, sol.eq] for sol in sols], ans) ans leadingDenomRicDE(c, l) == @@ -146,7 +146,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where not(empty?(ind := dmax(rec, c, l))) repeat ans := concat([rec.deg, getPol(rec, c, l, ind)], ans) done := concat(rec.deg, done) - sort_!(#1.deg > #2.deg, ans) + sort!(#1.deg > #2.deg, ans) getPol(rec, c, l, ind) == one?(rec.deg) => getPol1(ind, c, l) @@ -192,7 +192,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where not(empty?(ind := infmax(rec, l))) repeat ans := concat([rec.deg, getPoly(rec, l, ind)], ans) done := concat(rec.deg, done) - sort_!(#1.deg > #2.deg, ans) + sort!(#1.deg > #2.deg, ans) factoredDenomRicDE l == bd := factors balancedFactorisation(leadingCoefficient l, coefficients l) @@ -246,7 +246,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where sols := fracsol(neweq, zeros, rest lc) ans := empty? sols => concat(rec, ans) - concat_!([[rec.frac + sol.frac, sol.eq] for sol in sols], ans) + concat!([[rec.frac + sol.frac, sol.eq] for sol in sols], ans) ans -- returns [] if the solutions of l have no polynomial component @@ -254,7 +254,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where ans:List(POL) := empty() finite? and zero? b => ans lc := leadingCoefficientRicDE l - if finite? then lc := select_!(#1.deg <= b, lc) + if finite? then lc := select!(#1.deg <= b, lc) for rec in lc repeat for a in zeros(rec.eq) | a ~= 0 repeat atn:UP := monomial(a, rec.deg) @@ -262,7 +262,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where sols := polysol(neweq, (rec.deg - 1)::N, true, zeros) ans := empty? sols => concat([atn, neweq], ans) - concat_!([[atn + sol.poly, sol.eq] for sol in sols], ans) + concat!([[atn + sol.poly, sol.eq] for sol in sols], ans) ans @ @@ -404,7 +404,7 @@ RationalRicDE(F, UP): Exports == Implementation where for i in 0..n repeat ans := ans + monomial((sy := new s)::P, i::N) l := concat(sy, l) - [ans, reverse_! l] + [ans, reverse! l] ratsln l == ls:List(SY) := empty() @@ -489,7 +489,7 @@ RationalRicDE(F, UP): Exports == Implementation where n := degree l ans:List(QF) := empty() for rec in singRicDE(l, ezfactor) repeat - ans := removeDuplicates_! concat_!(ans, + ans := removeDuplicates! concat!(ans, [rec.frac + f for f in nonSingSolve(n, rec.eq, zeros)]) #ans = n => return ans ans @@ -499,7 +499,7 @@ RationalRicDE(F, UP): Exports == Implementation where nonSingSolve(n, l, zeros) == ans:List(QF) := empty() for rec in polyRicDE(l, zeros) repeat - ans := removeDuplicates_! concat_!(ans, nopoly(n,rec.poly,rec.eq,zeros)) + ans := removeDuplicates! concat!(ans, nopoly(n,rec.poly,rec.eq,zeros)) #ans = n => return ans ans @@ -512,7 +512,7 @@ RationalRicDE(F, UP): Exports == Implementation where nopoly(n, p, l, zeros) == ans:List(QF) := empty() for rec in constantCoefficientRicDE(l, constantRic(#1, zeros)) repeat - ans := removeDuplicates_! concat_!(ans, + ans := removeDuplicates! concat!(ans, [(rec.constant::UP + p)::QF + f for f in logDerOnly(rec.eq)]) #ans = n => return ans ans |