* input - output: a, b * returns: * a := a/gcd(a,b), b := b/gcd(a,b) * and return value * 0 -> a != 1, b != 1 * 1 -> a == 1, b !

conversion of a GMP integer to number

returns TRUE if there were errors analyze inputs, check them for consistency detects nc_type, DO NOT initialize multiplication but call for it at the

pCmp: args may be NULL returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2)))

for a monomial p, returns the number of the last block */ where a nonzero exponent is sitting */

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CanonicalForm resultant ( const CanonicalForm & f, const CanonicalForm & g, const Variable & x ) * * resultant() - return resultant of f and g with

stolen from: https://graphics.stanford.edu/~seander/bithacks.html#IntegerLog

* define and execute a new ring which order is a lexicographic order * ***********************************************************************/

2 *deletes higher monomial of p, re-compute ecart and length *works only for orderings with ecart =pFDeg(end)-pFDeg(start) */

CanonicalForm getVars ( const CanonicalForm & f ) * * getVars() - get polynomial variables of f. * * Return the product of all of them, 1 if there

modifies a */ this is an intermediate simplification routine - not a comple "normalize" */

PolyhedralCone const& PolyhedralFan::highestDimensionalCone()const { return *cones.rbegin(); } */

splits a frame (e.g. x(1)*y(5)) m1 into m1 and m2 (e.g. m1=x(1) and m2=y(1)) at is the number of the block to split at, starting at 1

assume that there is a canonical subring in cf and we know that division is possible for these a and b in the subring, n_ExactDiv performs it, may ski

returns ceil(log_4(l))

compute a random element a of \f$ F_{p}(\alpha ) \f$ , s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns fail if there are no field ele

///////////////////////////////////////////////////////////////////// Creation/Destruction of buckets

* squarefree factorization **/

* return intvvec = (1,0, ..., 0) * **********************************/

Returns angles you have to rotate about y,x and z axis.

same as above, only with set S

returns m*p, does destroy p, preserves m

Take a given vector and normalise each entry to get a Euclidean distance of 1 between the zero vector and the vector itself.

normalize a poly, i.e. in char 0 clear denominators, remove integer content in char p divide by leading coeff

2 * create a number from int */