set "baseuri" "cic:/matita/CoRN-Decl/algebra/CPoly_Degree".
+include "CoRN.ma".
+
(* $Id: CPoly_Degree.v,v 1.5 2004/04/23 10:00:53 lcf Exp $ *)
-(* INCLUDE
-CPoly_NthCoeff
-*)
+include "algebra/CPoly_NthCoeff.ma".
-(* INCLUDE
-CFields
-*)
+include "algebra/CFields.ma".
(*#* *Degrees of Polynomials
** Degrees of polynomials over a ring
*)
(* UNEXPORTED
-Section Degree_def.
+Section Degree_def
*)
-inline cic:/CoRN/algebra/CPoly_Degree/R.var.
+alias id "R" = "cic:/CoRN/algebra/CPoly_Degree/Degree_def/R.var".
(* begin hide *)
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
(* end hide *)
(*#*
coefficient is [[#]Zero])!
*)
-inline cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/lth_of_poly.con".
(*#*
When dealing with constructive polynomials, notably over the reals or
that the `degree is at most [j]'.
*)
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic.con".
-inline cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/odd_cpoly.con".
-inline cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/even_cpoly.con".
-inline cic:/CoRN/algebra/CPoly_Degree/regular.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/regular.con".
(* UNEXPORTED
-End Degree_def.
+End Degree_def
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Degree_props.
+Section Degree_props
*)
-inline cic:/CoRN/algebra/CPoly_Degree/R.var.
+alias id "R" = "cic:/CoRN/algebra/CPoly_Degree/Degree_props/R.var".
(* begin hide *)
+(* NOTATION
+Notation RX := (cpoly_cring R).
+*)
+
(* end hide *)
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_wd.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_wd.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_wd.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_wd.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_wd.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_imp_degree_le.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_c_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_c_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_c_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_c_one.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_x_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_x_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_x_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_x_.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_x_.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_mon.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_inv.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_plus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_minus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/Sum_degree_le.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_inv.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_inv.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_plus_rht.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_minus_lft.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_plus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_plus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_minus.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_minus.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult_aux.con".
(* UNEXPORTED
Hint Resolve degree_mult_aux: algebra.
*)
-inline cic:/CoRN/algebra/CPoly_Degree/monic_mult.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_mult.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_nexp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_nexp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/lt_i_lth_of_poly.con".
-inline cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_degree_lth.con".
-inline cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/Cpoly_ex_degree.con".
-inline cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum''.con".
(* UNEXPORTED
Hint Resolve poly_as_sum'': algebra.
*)
-inline cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum'.con".
-inline cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/poly_as_sum.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_zero.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_1_imp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_cpoly_linear.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_cpoly_linear.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_one.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_one.con".
-inline cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con".
(* UNEXPORTED
-End Degree_props.
+End Degree_props
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section degree_props_Field.
+Section degree_props_Field
*)
(*#* ** Degrees of polynomials over a field
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CPoly_Degree/F.var.
+alias id "F" = "cic:/CoRN/algebra/CPoly_Degree/degree_props_Field/F.var".
(* begin hide *)
+(* NOTATION
+Notation FX := (cpoly_cring F).
+*)
+
(* end hide *)
-inline cic:/CoRN/algebra/CPoly_Degree/degree_mult.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_nexp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_le_mult_imp.con".
-inline cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con.
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con".
(* UNEXPORTED
-End degree_props_Field.
+End degree_props_Field
*)