/usr/share/axiom-20170501/src/algebra/PDRING.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | )abbrev category PDRING PartialDifferentialRing
++ Description:
++ A partial differential ring with differentiations indexed by a
++ parameter type S.
++
++ Axioms\br
++ \tab{5}\spad{differentiate(x+y,e)=differentiate(x,e)+differentiate(y,e)}\br
++ \tab{5}\spad{differentiate(x*y,e)=x*differentiate(y,e)+differentiate(x,e)*y}
PartialDifferentialRing(S) : Category == SIG where
S : SetCategory
SIG ==> Ring with
differentiate : (%, S) -> %
++ differentiate(x,v) computes the partial derivative of x
++ with respect to v.
differentiate : (%, List S) -> %
++ differentiate(x,[s1,...sn]) computes successive partial
++ derivatives,
++ that is, \spad{differentiate(...differentiate(x, s1)..., sn)}.
differentiate : (%, S, NonNegativeInteger) -> %
++ differentiate(x, s, n) computes multiple partial derivatives,
++ that is, n-th derivative of x with respect to s.
differentiate : (%, List S, List NonNegativeInteger) -> %
++ differentiate(x, [s1,...,sn], [n1,...,nn]) computes
++ multiple partial derivatives, that is, \spad{D(...D(x, s1)..., sn)}.
D : (%, S) -> %
++ D(x,v) computes the partial derivative of x
++ with respect to v.
D : (%, List S) -> %
++ D(x,[s1,...sn]) computes successive partial derivatives,
++ that is, \spad{D(...D(x, s1)..., sn)}.
D : (%, S, NonNegativeInteger) -> %
++ D(x, s, n) computes multiple partial derivatives, that is,
++ n-th derivative of x with respect to s.
D : (%, List S, List NonNegativeInteger) -> %
++ D(x, [s1,...,sn], [n1,...,nn]) computes
++ multiple partial derivatives, that is,
++ \spad{D(...D(x, s1, n1)..., sn, nn)}.
add
differentiate(r:%, l:List S) ==
for s in l repeat r := differentiate(r, s)
r
differentiate(r:%, s:S, n:NonNegativeInteger) ==
for i in 1..n repeat r := differentiate(r, s)
r
differentiate(r:%, ls:List S, ln:List NonNegativeInteger) ==
for s in ls for n in ln repeat r := differentiate(r, s, n)
r
D(r:%, v:S) == differentiate(r,v)
D(r:%, lv:List S) == differentiate(r,lv)
D(r:%, v:S, n:NonNegativeInteger) == differentiate(r,v,n)
D(r:%, lv:List S, ln:List NonNegativeInteger) == differentiate(r, lv, ln)
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