diff options
Diffstat (limited to 'src/algebra/riccati.spad.pamphlet')
| -rw-r--r-- | src/algebra/riccati.spad.pamphlet | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/src/algebra/riccati.spad.pamphlet b/src/algebra/riccati.spad.pamphlet index 30485093..877d0403 100644 --- a/src/algebra/riccati.spad.pamphlet +++ b/src/algebra/riccati.spad.pamphlet @@ -128,7 +128,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where lc := leadingDenomRicDE(c, op) if finite? then lc := select_!(#1.deg <= b, lc) for rec in lc repeat - for r in zeros(c, rec.eq) | r ^= 0 repeat + for r in zeros(c, rec.eq) | r ~= 0 repeat rcn := r /$RF (c ** rec.deg) neweq := changeVar(op, rcn) sols := padicsol(c, neweq, (rec.deg-1)::N, true, zeros) @@ -163,7 +163,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where constantCoefficientOperator(op, m) == ans:UP := 0 - while op ^= 0 repeat + while op ~= 0 repeat if degree(p := leadingCoefficient op) = m then ans := ans + monomial(leadingCoefficient p, degree op) op := reductum op @@ -179,7 +179,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where i := first(rec.ij) m := i * (d := rec.deg) + nu coefficient(l, i::N) ans:List(Z) := empty() - for j in 0..n | (f := coefficient(l, j)) ^= 0 repeat + for j in 0..n | (f := coefficient(l, j)) ~= 0 repeat if ((k := (j * d + nu f)) > m) then return empty() else if (k = m) then ans := concat(j, ans) ans @@ -226,8 +226,8 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where innerlb(l, nu) == lb:List(IJ) := empty() n := degree l - for i in 0..n | (li := coefficient(l, i)) ^= 0repeat - for j in i+1..n | (lj := coefficient(l, j)) ^= 0 repeat + for i in 0..n | (li := coefficient(l, i)) ~= 0repeat + for j in i+1..n | (lj := coefficient(l, j)) ~= 0 repeat u := (nu li - nu lj) exquo (i-j) if (u case Z) and ((b := u::Z) > 0) then lb := concat([[i, j], b::N], lb) @@ -257,7 +257,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where lc := leadingCoefficientRicDE l if finite? then lc := select_!(#1.deg <= b, lc) for rec in lc repeat - for a in zeros(rec.eq) | a ^= 0 repeat + for a in zeros(rec.eq) | a ~= 0 repeat atn:UP := monomial(a, rec.deg) neweq := changeVar(l, atn) sols := polysol(neweq, (rec.deg - 1)::N, true, zeros) @@ -430,8 +430,8 @@ RationalRicDE(F, UP): Exports == Implementation where ans:List(POL) := [[0, l]] empty?(lc := leadingCoefficientRicDE l) => ans rec := first lc -- one with highest degree - for a in zeros(rec.eq) | a ^= 0 repeat - if (p := newtonSolution(l, a, rec.deg, zeros)) ^= 0 then + for a in zeros(rec.eq) | a ~= 0 repeat + if (p := newtonSolution(l, a, rec.deg, zeros)) ~= 0 then ans := concat([p, changeVar(l, p)], ans) ans @@ -439,7 +439,7 @@ RationalRicDE(F, UP): Exports == Implementation where reverseUP p == ans:UTS := 0 n := degree(p)::Z - while p ^= 0 repeat + while p ~= 0 repeat ans := ans + monomial(leadingCoefficient p, (n - degree p)::N) p := reductum p ans @@ -454,11 +454,11 @@ RationalRicDE(F, UP): Exports == Implementation where m:Z := 0 aeq:UPS := 0 op := l - while op ^= 0 repeat + while op ~= 0 repeat mu := degree(op) * n + degree leadingCoefficient op op := reductum op if mu > m then m := mu - while l ^= 0 repeat + while l ~= 0 repeat c := leadingCoefficient l d := degree l s:UTS := monomial(1, (m - d * n - degree c)::N)$UTS * reverseUP c |