diff options
Diffstat (limited to 'src/algebra/odeef.spad.pamphlet')
| -rw-r--r-- | src/algebra/odeef.spad.pamphlet | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/src/algebra/odeef.spad.pamphlet b/src/algebra/odeef.spad.pamphlet index 1b1cc186..5598124b 100644 --- a/src/algebra/odeef.spad.pamphlet +++ b/src/algebra/odeef.spad.pamphlet @@ -52,7 +52,7 @@ ReductionOfOrder(F, L): Exports == Impl where empty? sols => [l, empty()] neweq := ReduceOrder(l, sol := first sols) rec := ReduceOrder(neweq, [diff(s / sol) for s in rest sols]) - [rec.eq, concat_!(rec.op, sol)] + [rec.eq, concat!(rec.op, sol)] ithcoef(eq, i, s) == ans:F := 0 @@ -65,9 +65,9 @@ ReductionOfOrder(F, L): Exports == Impl where ReduceOrder(eq:L, sol:F) == s:A := new(n := degree eq, 0) -- will contain derivatives of sol si := sol -- will run through the derivatives - qsetelt_!(s, 0, si) + qsetelt!(s, 0, si) for i in 1..(n-1)::NonNegativeInteger repeat - qsetelt_!(s, i, si := diff si) + qsetelt!(s, i, si := diff si) ans:L := 0 for i in 0..(n-1)::NonNegativeInteger repeat ans := ans + monomial(ithcoef(eq, i, s), i) @@ -203,7 +203,7 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where -- xpart(f,x) removes any constant not involving x from f xpart(f, x) == - l := reverse_! varselect(tower f, x) + l := reverse! varselect(tower f, x) lp := [k::P for k in l] smpxpart(numer f, x, l, lp) / smpxpart(denom f, x, l, lp) @@ -235,14 +235,14 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where rec := ReduceOrder(oper, sols) le := expsols(rec.eq, k, x) int:List(F) := [xpart(multivariate(h, k), x) for h in rec.op] - concat_!([xpart(multivariate(h, k), x) for h in sols], + concat!([xpart(multivariate(h, k), x) for h in sols], [multint(e, int, x) for e in le]) homosolve1(oper, sols, k, x) == zero?(n := (degree(oper) - #sols)::N) => sols -- all solutions found rec := ReduceOrder(oper, sols) int:List(F) := [xpart(h, x) for h in rec.op] - concat_!(sols, [multint(e, int, x) for e in norf1(rec.eq, k, x, n::N)]) + concat!(sols, [multint(e, int, x) for e in norf1(rec.eq, k, x, n::N)]) -- if the coefficients are rational functions, then the equation does not -- not have a proper 1st-order right factor over the rational functions @@ -289,7 +289,7 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where -- left hand side has rational coefficients rfSolve(eq, g, k, x) == op := ulodo(eq, k) - empty? remove_!(k, varselect(kernels g, x)) => -- i.e. rhs is rational + empty? remove!(k, varselect(kernels g, x)) => -- i.e. rhs is rational rc := ratDsolve(op, univariate(g, k)) rc.particular case "failed" => -- this implies g ~= 0 doVarParams(eq, g, homosolve(eq, op, rc.basis, k, x), x) @@ -305,7 +305,7 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where for i in minIndex v .. maxIndex v for yy in y0 repeat v.i := yy - eval(h, kx, a) h := diff h - (sol := particularSolution(map_!(eval(#1,kx,a),wronskianMatrix(b,n)), v)) + (sol := particularSolution(map!(eval(#1,kx,a),wronskianMatrix(b,n)), v)) case "failed" => "failed" for f in b for i in minIndex(s := sol::V) .. repeat hp := hp + s.i * f @@ -510,7 +510,7 @@ ElementaryFunctionODESolver(R, F): Exports == Implementation where for eq in eqs repeat (u := parseSYSeq(eq,lk0,lk1,lf,x)) case "failed" => return "failed" rec := u::ROW - setRow_!(m, rec.index, rec.row) + setRow!(m, rec.index, rec.row) v(rec.index) := rec.rh [m, v] |