Accessing MAGMA from Maple

November 29 2005 Alec Mihailovs 4065
Maple

2

Similarly to searching of digits of π, Maple can access other Internet resources. In particular, here is an example of accessing MAGMA through William Stein's online SAGE/MAGMA/PARI calculator,
Magma:=proc(x) 
local s,a,b;
uses StringTools, Sockets;
s:=Open("modular.ucsd.edu",80);
Write(s,cat("GET /cgi-bin/calc/calc.py?with=MAGMA&input=",
            map((c->cat("%",c))@convert,convert(Squeeze(x),bytes),hex)[],
            " HTTP/1.0\n\n"));
a := "";
		b := Read(s):
		while b <> false do
			a := cat(a,b);
			b := Read(s):
		end do;
Close(s);
a[Search("--",a)..Search("Total",a)-1]
end:
For example (taken from recent Dave Rusin posting in sci.math.symbolic),
Magma("Q:=GaloisField(35098201); P<x,y>:=PolynomialRing(Q,2); 
I:=ideal<P| y + (1+x^5+x^10), x^34 +1 >; Groebner(I); I;");

  "-------------------------------------

        Ideal of Polynomial ring of rank 2 over GF(35098201)
        Lexicographical Order
        Variables: x, y
        Dimension 0
        Groebner basis:
        [
            x + 33784728*y^33 + 15744019*y^32 + 14466235*y^31 + 14\
        937582*y^30 +
                9988153*y^29 + 24849537*y^28 + 13827463*y^27 + 108\
        51940*y^26 +
                25333828*y^25 + 29238403*y^24 + 35087366*y^23 + 31\
        85785*y^22 +
                12125255*y^21 + 11305600*y^20 + 713800*y^19 + 1188\
        2241*y^18 +
                23388419*y^17 + 12677392*y^16 + 20159861*y^15 + 31\
        143912*y^14 +
                33062327*y^13 + 11580434*y^12 + 10629964*y^11 + 14\
        094725*y^10 +
                30606411*y^9 + 20913610*y^8 + 23355486*y^7 + 32139\
        384*y^6 + 35026862*y^5
                + 11038274*y^4 + 26690476*y^3 + 752845*y^2 + 95143\
        80*y + 16409093,
            y^34 + 34*y^33 + 561*y^32 + 5984*y^31 + 46376*y^30 + 2\
        78256*y^29 +
                1344904*y^28 + 5379616*y^27 + 18156204*y^26 + 1735\
        3055*y^25 +
                25833537*y^24 + 5312152*y^23 + 21881025*y^22 + 154\
        30534*y^21 +
                23145801*y^20 + 30861068*y^19 + 27872968*y^18 + 17\
        124952*y^17 +
                27873223*y^16 + 30858484*y^15 + 23140973*y^14 + 15\
        452362*y^13 +
                21951303*y^12 + 5362540*y^11 + 25762851*y^10 + 171\
        84126*y^9 +
                18014271*y^8 + 5332492*y^7 + 1358334*y^6 + 297330*\
        y^5 + 54824*y^4 +
                7259*y^3 + 714*y^2 + 34*y + 1
        ]

        "
Presumably this is a wrong answer, see Dave Rusin posting cited above.
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