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D.7.2.3 ures_solve
Procedure from library solve.lib (see solve_lib).
- Usage:
ures_solve(i [, k, p] ); i = ideal, k, p = integers
k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky, k=1: use resultant matrix of Macaulay which works only for homogeneous ideals, p>0: defines precision of the long floats for internal computation if the basering is not complex (in decimal digits), (default: k=0, p=30)- Assume:
i is a zerodimensional ideal with
nvars(basering) = ncols(i) = number of vars
actually occurring in i,- Return:
list of all (complex) roots of the polynomial system i = 0; the result is of type
string: if the basering is not complex, number: otherwise.
Example:
LIB "solve.lib"; // compute the intersection points of two curves ring rsq = 0,(x,y),lp; ideal gls= x2 + y2 - 10, x2 + xy + 2y2 - 16; ures_solve(gls,0,16); → [1]: → [1]: → 1 → [2]: → -3 → [2]: → [1]: → -1 → [2]: → 3 → [3]: → [1]: → 2.82842712474619 → [2]: → 1.414213562373095 → [4]: → [1]: → -2.82842712474619 → [2]: → -1.414213562373095 // result is a list (x,y)-coordinates as strings // now with complex coefficient field, precision is 20 digits ring rsc= (real,20,I),(x,y),lp; ideal i = (2+3*I)*x2 + (0.35+I*45.0e-2)*y2 - 8, x2 + xy + (42.7)*y2; list l= ures_solve(i,0,10); // result is a list of (x,y)-coordinates of complex numbers l; → [1]: → [1]: → (-1.315392899374542198+I*0.70468233142752928117) → [2]: → (0.12292646536251281054+I*0.19245727404407015049) → [2]: → [1]: → (1.315392899374542198-I*0.70468233142752928117) → [2]: → (-0.12292646536251281054-I*0.19245727404407015049) → [3]: → [1]: → (1.31584587549391830705-I*0.70396753310002259573) → [2]: → (0.092006639590217681983+I*0.20902112035965287775) → [4]: → [1]: → (-1.31584587549391830705+I*0.70396753310002259573) → [2]: → (-0.092006639590217681983-I*0.20902112035965287775) // check the result subst(subst(i[1],x,l[1][1]),y,l[1][2]); → 0 |