> Clearly the alternatives are not equvalent. AFAICS Symbol
> version catches all operators with given name. Operator
> will catch some. Have to think which one behaves better.
This attachment is a preliminary patch that fixes 'eval' for
BasicOperator arguments.
I found this bug from cos2sec (and etc.) of manip.spad.
There are many usages of 'eval' that take Symbol as argument.
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diff --git a/src/algebra/fspace.spad b/src/algebra/fspace.spad
index 6cd8bab2..e96de163 100644
--- a/src/algebra/fspace.spad
+++ b/src/algebra/fspace.spad
@@ -226,7 +226,7 @@ ExpressionSpace() : Category == Defn where
elt(op : OP, x : %, y : %, z : %, t : %, s : %, r : %, q : %,
p : %, o : %) == op [x, y, z, t, s, r, q, p, o]
eval(x : %, s : SY, f : List % -> %) == eval(x, [s], [f])
- eval(x : %, s : OP, f : List % -> %) == eval(x, [name s], [f])
+ eval(x : %, s : OP, f : List % -> %) == eval(x, [s], [f])
eval(x : %, s : SY, f : % -> %) ==
eval(x, [s], [(y : List %) : % +-> f(first y)])
eval(x : %, s : OP, f : % -> %) ==
@@ -239,8 +239,8 @@ ExpressionSpace() : Category == Defn where
eval(x : %, ls : List SY, lf : List(% -> %)) ==
eval(x, ls, [y +-> f(first y) for f in lf]$List(List % -> %))
- eval(x : %, ls : List OP, lf : List(List % -> %)) ==
- eval(x, [name s for s in ls]$List(SY), lf)
+ --eval(x : %, ls : List OP, lf : List(List % -> %)) ==
+ -- eval(x, [name s for s in ls]$List(SY), lf) -- wrong
map(fn, k) ==
(l := [fn x for x in argument k]$List(%)) = argument k => k::%
@@ -503,6 +503,10 @@ FunctionSpace(R : Comparable) : Category == Definition where
++ eval(x, [s1, ..., sm], [n1, ..., nm], [f1, ..., fm]) replaces
++ every \spad{si(a1, ..., an)^ni} in x by \spad{fi(a1, ..., an)}
++ for any a1, ..., am.
+ eval : (%, List OP, List N, List(List % -> %)) -> %
+ ++ eval(x, [s1, ..., sm], [n1, ..., nm], [f1, ..., fm]) replaces
+ ++ every \spad{si(a1, ..., an)^ni} in x by \spad{fi(a1, ..., an)}
+ ++ for any a1, ..., am.
eval : (%, SY, N, List % -> %) -> %
++ eval(x, s, n, f) replaces every \spad{s(a1, ..., am)^n} in x
++ by \spad{f(a1, ..., am)} for any a1, ..., am.
@@ -579,6 +583,7 @@ FunctionSpace(R : Comparable) : Category == Definition where
diffEval : List % -> %
dfeval : (List %, K) -> %
smprep : (List SY, List N, List(List % -> %), MP) -> %
+ smprep2 : (List OP, List N, List(List % -> %), MP) -> %
diffdiff : (List %, SY) -> %
subs : (% -> %, K) -> %
symsub : (SY, Z) -> SY
@@ -658,6 +663,7 @@ FunctionSpace(R : Comparable) : Category == Definition where
eval(x, [s], [n], [(y : List %) : % +-> f(first(y))])
eval(x : %, s : SY, n : N, f : List % -> %) == eval(x, [s], [n], [f])
eval(x : %, l : List SY, f : List(List % -> %)) == eval(x, l, new(#l, 1), f)
+ eval(x : %, l : List OP, f : List(List % -> %)) == eval(x, l, new(#l, 1), f)
elt(op : OP, args : List %) ==
unary? op and ((od? := has?(op, ODD)) or has?(op, EVEN)) and
@@ -692,6 +698,27 @@ FunctionSpace(R : Comparable) : Category == Definition where
q := reductum q
a
+ smprep2(lop, lexp, lfunc, p) ==
+ (v := mainVariable p) case "failed" => p::%
+ -- symbolIfCan(k := v::K) case SY => p::%
+ k := v::K
+ g := (op := operator k)
+ (arg := [eval(a, lop, lexp, lfunc) for a in argument k]$List(%))
+ q := map(y +-> eval(y::%, lop, lexp, lfunc),
+ univariate(p, k))$SparseUnivariatePolynomialFunctions2(MP, %)
+ (n := position(op, lop)) < minIndex lop => q g
+ a : % := 0
+ f := eval((lfunc.n) arg, lop, lexp, lfunc)
+ e := lexp.n
+ while q ~= 0 repeat
+ m := degree q
+ qr := divide(m, e)
+ t1 := f ^ (qr.quotient)::N
+ t2 := g ^ (qr.remainder)::N
+ a := a + leadingCoefficient(q) * t1 * t2
+ q := reductum q
+ a
+
dispdiff l ==
s := second(l)::O
t := third(l)::O
@@ -1022,6 +1049,9 @@ FunctionSpace(R : Comparable) : Category == Definition where
eval(x : %, s : List SY, n : List N, f : List(List % -> %)) ==
smprep(s, n, f, numer x)
+ eval(x : %, s : List OP, n : List N, f : List(List % -> %)) ==
+ smprep2(s, n, f, numer x)
+
isPlus x ==
(u := isPlus numer x) case "failed" => "failed"
[p::% for p in u::List(MP)]
@@ -1123,6 +1153,9 @@ FunctionSpace(R : Comparable) : Category == Definition where
eval(x : %, s : List SY, n : List N, f : List(List % -> %)) ==
smprep(s, n, f, numer x) / smprep(s, n, f, denom x)
+ eval(x : %, s : List OP, n : List N, f : List(List % -> %)) ==
+ smprep2(s, n, f, numer x) / smprep2(s, n, f, denom x)
+
differentiate(f : %, x : SY) ==
(smpderiv(numer f, x) * denom(f)::% -
numer(f)::% * smpderiv(denom f, x))
