X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Falgebra%2FCPoly_ApZero.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Falgebra%2FCPoly_ApZero.ma;h=9a72ec02a9e6c4768d9541958a9578ea1c42df07;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma b/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma new file mode 100644 index 000000000..9a72ec02a --- /dev/null +++ b/matita/contribs/CoRN-Decl/algebra/CPoly_ApZero.ma @@ -0,0 +1,194 @@ +(**************************************************************************) +(* ___ *) +(* ||M|| *) +(* ||A|| A project by Andrea Asperti *) +(* ||T|| *) +(* ||I|| Developers: *) +(* ||T|| The HELM team. *) +(* ||A|| http://helm.cs.unibo.it *) +(* \ / *) +(* \ / This file is distributed under the terms of the *) +(* v GNU General Public License Version 2 *) +(* *) +(**************************************************************************) + +(* This file was automatically generated: do not edit *********************) + +set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_ApZero". + +include "CoRN.ma". + +(* $Id: CPoly_ApZero.v,v 1.3 2004/04/23 10:00:53 lcf Exp $ *) + +include "algebra/CPoly_Degree.ma". + +include "algebra/COrdFields2.ma". + +(*#* * Polynomials apart from zero *) + +inline "cic:/CoRN/algebra/CPoly_ApZero/distinct1.con". + +(* UNEXPORTED +Implicit Arguments distinct1 [A]. +*) + +(* UNEXPORTED +Section Poly_Representation +*) + +(*#* +** Representation of polynomials +%\begin{convention}% Let [R] be a field, [RX] the ring of polynomials +over [R], [a_ : nat->R] with [(distinct1 a_)] and let [f] be a +polynomial over [R], [n] a natural with [(degree_le n f)], i.e. [f] +has degree at most [n]. +%\end{convention}% +*) + +alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var". + +alias id "a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var". + +alias id "distinct_a_" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var". + +alias id "f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var". + +alias id "n" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var". + +alias id "degree_f" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var". + +(* begin hide *) + +(* NOTATION +Notation RX := (cpoly_cring R). +*) + +(* end hide *) + +include "tactics/Transparent_algebra.ma". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_shifted.con". + +include "tactics/Opaque_algebra.ma". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_linear_factor.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/zero_poly.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/identical_poly.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_degree.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_zero.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor'_apzero.con". + +(* UNEXPORTED +Hint Resolve poly_01_factor'_zero. +*) + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_degree.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_zero.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_factor_one.con". + +(* UNEXPORTED +Hint Resolve poly_01_factor_zero poly_01_factor_one: algebra. +*) + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree'.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_degree.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_zero.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_01_one.con". + +(* UNEXPORTED +Hint Resolve poly_01_zero poly_01_one: algebra. +*) + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation''.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation'.con". + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_representation.con". + +(* UNEXPORTED +Hint Resolve poly_representation: algebra. +*) + +inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con". + +(* UNEXPORTED +End Poly_Representation +*) + +(* UNEXPORTED +Section Characteristic_zero +*) + +(*#* +If we are in a field of characteristic zero, the previous result can be +strengthened. +*) + +alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var". + +(* begin show *) + +alias id "H" = "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var". + +(* end show *) + +(* begin hide *) + +(* NOTATION +Notation RX := (cpoly_cring R). +*) + +(* end hide *) + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_apzero.con". + +(*#* +Also, in this situation polynomials are extensional functions. +*) + +inline "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con". + +(* UNEXPORTED +End Characteristic_zero +*) + +(*#* +** Polynomials are nonzero on any interval +*) + +(* UNEXPORTED +Section Poly_ApZero_Interval +*) + +alias id "R" = "cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var". + +(* begin hide *) + +(* NOTATION +Notation RX := (cpoly_cring R). +*) + +(* end hide *) + +inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con". + +(* UNEXPORTED +End Poly_ApZero_Interval +*) +