| /dports/math/gap/gap-4.11.0/pkg/NumericalSgps-1.2.1/gap/ |
| H A D | irreducibles.gd | 41 ## Produces an irreducible numerical semigroup by using
42 ## "Every positive integer is the Frobenius number of an irreducible...".
52 ## Computes the set of irreducible numerical semigroups with given
63 ## Computes the set of irreducible numerical semigroups with multipliciy m
87 ## Returns a list of irreducible numerical semigroups
100 ## Checks whether or not s is an irreducible numerical semigroup.
134 # semigroups from almost irreducible numerical semigroups, Comm. Algebra.
151 ## The argument is an irreducible numerical semigroup. The output is the set of
163 ## The arguments are an irreducible numerical semigroup and a
211 ## that is, the cardinality of a (any) minimal presentation equals
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| /dports/math/gap/gap-4.11.0/grp/ |
| H A D | imf.gd | 12 ## irreducible maximal finite integral matrix groups.
76 ## classes of irreducible maximal finite integral matrix groups in some
79 ## The default value of z is 1. If any of the arguments is zero, the routine
91 ## Q-class of the irreducible maximal finite integral matrix groups of
110 ## in the qth Q-class of irreducible maximal finite integral matrix groups
139 ## irreducible maximal finite integral matrix groups of dimension <dim>.
156 ## Q-class of the irreducible maximal finite integral matrix groups of
171 ## irreducible maximal finite subgroups of dimension dim, i. e., the number
172 ## of Q-classes of irreducible maximal finite subgroups of GL(dim,Z), if dim
173 ## is at most 11 or a prime, or the number of Q-classes of irreducible
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| /dports/math/gap/gap-4.11.0/pkg/irredsol-1.4/doc/ |
| H A D | recognition.tex | 14 This chapter describes some functions which, given an irreducible matrix
16 to that group, see Section~"Identification of irreducible groups".
19 {\GAP} library of irreducible soluble groups.
25 \Section{Identification of irreducible groups}\null
35 "IdIrreducibleSolubleMatrixGroup") will work for the irreducible matrix group <G>, and `false' othe…
51 If the matrix group <G> is soluble and irreducible over $F
53 $GL(<n>, <F>)$ of $<G>$ belongs to the data base of irreducible soluble groups in
83 Let <G> be an irreducible soluble matrix group over a finite field, and let
152 A library of irreducible soluble subgroups of $GL(n, p)$, where $p$ is a
212 of absolutely irreducible soluble subgroups of $GL(<n>, <q>)$.
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| H A D | matgroups.tex | 45 Let <G> be an irreducible subgroup of $GL(n, F)$, where $F = `FieldOfMatrixGroup'(<G>)$
48 that the natural $E G$-module $E^n$ is the direct sum of absolutely irreducible $E G$-
49 submodules. The number of these absolutely irreducible summands equals the dimension of $E$
87 The matrix group <G> of degree <d> is irreducible over the field <F> if no subspace of $<F>^d$ is
105 … present, this operation returns true if <G> is absolutely irreducible, i.~e., irreducible over any
145 which are irreducible over <F> are available.
160 An irreducible matrix group <G> of degree <d> is primitive over the field <F> if it
178 irreducible matrix group <G> over the field <F>. If <F> is not given,
222 If <G> is an irreducible matrix group over a finite field then, by a theorem of Brauer, <G>
237 only methods available for irreducible matrix groups <G> over finite fields
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| H A D | access.tex | 27 lists of irreducible subgroups of $GL(<n>, <q>)$ but
32 \item{$\bullet$} each group in ${\cal A}_{n,q}$ is absolutely irreducible and
36 irreducible soluble subgroup of $GL(n, q)$
47 irreducible soluble subgroups of $GL(n,q)$ with trace field $\F_q$.
51 theorem of Brauer, an irreducible subgroup of $GL(n, q)$ with trace field $\F_{q_0}$
72 irreducible groups in the {\IRREDSOL} group library.
183 This function returns a list of all irreducible soluble matrix
231 # get all irreducible subgroups
236 # get only maximal absolutely irreducible ones
242 # get only absolutely irreducible groups
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| /dports/math/pari/pari-2.13.3/src/functions/polynomials/ |
| H A D | thueinit | 13 $P$ must either have at least two distinct irreducible factors over $\Q$,
14 or have one irreducible factor $T$ with degree $>2$ or two conjugate
25 @eprog\noindent The hardest case is when $\deg P > 2$ and $P$ is irreducible
31 cases where $P$ is reducible (not a pure power of an irreducible), \emph{or}
49 \misctitle{Note} It is sometimes possible to circumvent the above, and in any
63 \misctitle{Note} When $P$ is irreducible without a real root, the equation
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| /dports/math/octave-forge-queueing/queueing/inst/ |
| H A D | ctmcisir.m | 8 ## License, or (at your option) any later version.
25 ## @cindex irreducible Markov chain
27 ## Check if @var{Q} is irreducible, and identify Strongly Connected
48 ## 1 if @var{Q} is irreducible, 0 otherwise.
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| H A D | dtmcisir.m | 8 ## License, or (at your option) any later version.
25 ## @cindex irreducible Markov chain
27 ## Check if @var{P} is irreducible, and identify Strongly Connected
46 ## 1 if @var{P} is irreducible, 0 otherwise (scalar)
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| H A D | dtmcfpt.m | 8 ## License, or (at your option) any later version.
29 ## for an irreducible discrete-time Markov chain over the state space
38 ## @var{P} must be an irreducible stochastic matrix, which means that
84 if ( any(diag(P) == 1) )
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| /dports/math/lidia/lidia-2.3.0+latte-patches-2014-10-04/doc/ |
| H A D | field.tex | 24 a root of a monic irreducible polynomial with coefficients in the rational integers.
47 initializes with the given polynomial. If the given polynomial is not irreducible or not
56 % If this polynomial is not irreducible or not monic, the
58 If this polynomial is not irreducible or not monic, this results in undefined behaviour.
169 be monic and irreducible. The powers $\{1, b, b^2, \dots, b^{n-1}\}$ of $b$ will be used as
172 \item You may give a pair of a (monic and irreducible) generating polynomial $f$ and a
178 any matrix over the rationals would be an acceptable transformation matrix we use a
179 \code{bigint_matrix} (supporting any format supported by \code{bigint_matrix}) that is
228 As for the previous formats, any format supported by \code{bigint_matrix} can be used.
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| /dports/math/gap/gap-4.11.0/pkg/cvec-2.7.4/gap/ |
| H A D | linalg.gd | 96 # Returns a list with the irreducible factors of the characteristic
107 # irreds: set of the irreducible factors of the char. poly
108 # mult: multiplicities of the irreducible factors in the char. poly
110 # multmin: multiplicities of the irreducible factors in the minimal poly
134 ## or (at your option) any later version.
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| /dports/math/gap/gap-4.11.0/lib/ |
| H A D | ctblsolv.gd | 52 ## the normal subgroup such that the result describes the irreducible
54 ## (so <E>all</E> irreducible nonlinear representations are described
69 ## a list of nonlinear irreducible representations,
84 ## irreducible representations for abelian by supersolvable groups;
86 ## implementation computes the irreducible representations of the factor
103 ## An irreducible representation of <M>G_{i+1}</M> has either
105 ## or the induced representation is irreducible in <M>G_i</M>.
116 ## into a direct sum of irreducible representations of <M>G_{i+1}</M>.
159 ## (for example preserving a unitary form) in any way.
366 ## all irreducible characters of <A>G</A> are returned.
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| H A D | ctblgrp.gd | 21 ## If irreducible characters are missing afterwards,
28 ## but not the irreducible characters.
42 ## The computation of irreducible characters from the group needs to
117 ## routines to compute the irreducible characters and related information
182 ## This function takes a list of irreducible characters <A>new</A>,
213 ## even irreducible ones. Since the recalculation of characters is only
315 ## uses it to split character spaces and stores all the irreducible
343 ## unbinds components in the Dixon record that are not of use any longer.
344 ## It returns a list of irreducible characters.
361 ## computes the irreducible characters of the finite group <A>G</A>,
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| H A D | ctblmono.gd | 50 ## which is an irreducible constituent of a nonhomogeneous restriction
236 ## i.e., is a multiple of an irreducible character.
255 ## irreducible constituent of the restriction,
301 ## not induced from any proper subgroup, and <K>false</K> otherwise.
432 ## ordinary irreducible character of <M>G</M> is monomial.
550 ## irreducible.
643 ## <A>chi</A> is not induced from the inertia subgroup of a component of any
648 ## irreducible character.
704 ## An irreducible character of the group <M>G</M> is called
773 ## an irreducible character <A>chi</A> of a SM group <M>G</M>,
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| /dports/math/pari/pari-2.13.3/src/functions/number_fields/ |
| H A D | rnfpseudobasis | 5 Help: rnfpseudobasis(nf,T): given an irreducible polynomial T with
10 \kbd{nfinit}, and a monic irreducible polynomial $T$ in $\Z_K[x]$ defining a
56 And might have been nonmaximal at any other prime ideal $\goth{p}$ such
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| /dports/security/libecc/libecc-0.14.0/doc/ |
| H A D | polynomial.dox | 45 where adding the \zero to any element gives that same element, multiplying \zero
46 with any element gives \zero and multiplying \one with any element gives that
98 for any
144 closed under addition and multiplication (closed means that adding/multiplying any two
158 Also note that the characteristic of the field is still 5: adding any polynomial 5 times to
202 Likewise, when any two polynomials of <SPAN class="formula">t</SPAN> have a difference that can be
293 The reduction polynomial could be any irreducible polynomial, but by using a trinomial
304 for any <SPAN class="formula">a</SPAN> and <SPAN class="formula">b</SPAN> element of the field.
316 <H3>Finding an irreducible trinomial</H3>
348 which is more restrictive than irreducible. The chance that an arbitrary irreducible
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| /dports/math/gap/gap-4.11.0/pkg/recog-1.3.2/misc/obsolete/ |
| H A D | derived.gi | 29 # We assume G to act absolutely irreducible
62 # the irreducible N-submodule is absolutely irreducible!
109 ## (at your option) any later version.
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| /dports/science/nwchem-data/nwchem-7.0.2-release/doc/prog/ |
| H A D | symmetry.tex | 166 integer nir ! [output] Returns no. irreducible reps.
174 number of irreducible representations (\verb+nir+), the name of each
175 irreducible representation (\verb+zir(i)+, \verb+i=1,...,nir+), the
186 The maximum number of irreducible representations in any point group
200 All is simple except for complex conjugate pairs of irreducible
226 Returns in \verb+nbf_per_ir+ the number of functions per irreducible
228 maximim number of irreducible represenations in any point group is 20.
240 returning in \verb+irs(i)+ the number of the irreducible
331 not incorporate any factors into \verb+q2+ to account for this (i.e.,
348 incorporate any additional factors into \verb+q4+ (i.e., \verb+q4+
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| /dports/science/nwchem/nwchem-7b21660b82ebd85ef659f6fba7e1e73433b0bd0a/doc/prog/ |
| H A D | symmetry.tex | 166 integer nir ! [output] Returns no. irreducible reps.
174 number of irreducible representations (\verb+nir+), the name of each
175 irreducible representation (\verb+zir(i)+, \verb+i=1,...,nir+), the
186 The maximum number of irreducible representations in any point group
200 All is simple except for complex conjugate pairs of irreducible
226 Returns in \verb+nbf_per_ir+ the number of functions per irreducible
228 maximim number of irreducible represenations in any point group is 20.
240 returning in \verb+irs(i)+ the number of the irreducible
331 not incorporate any factors into \verb+q2+ to account for this (i.e.,
348 incorporate any additional factors into \verb+q4+ (i.e., \verb+q4+
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| /dports/math/gap/gap-4.11.0/pkg/sonata-2.9.1/doc/ref/ |
| H A D | fpf.tex | 54 The order of any fpf automorphism group <phi> on <G> divides <kmax>.
127 returns the degree of the irreducible fpf representations of
141 returns the degree of the irreducible fpf representations of
147 All irreducible fpf representations of the metacyclic group
162 returns the degree of the irreducible fpf representations of
182 returns the degree of the irreducible fpf representations of
188 All irreducible fpf representations of this group
201 returns the degree of the irreducible fpf representations of
226 is irreducible and fpf.
228 representations up to equivalence; each irreducible fpf
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| /dports/math/frobby/frobby-0.9.1/test/messages/ |
| H A D | help-optimize.err | 6 maximize v * e such that e encodes an irreducible component of I,
9 irreducible ideal by being the exponent vector of the product of the
12 The input is composed of the ideal I in any format, optionally followed by the
62 for monomials representing irreducible components.
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| /dports/math/gap/gap-4.11.0/pkg/irredsol-1.4/ |
| H A D | README | 5 IRREDSOL is a GAP package which provides a library of all irreducible
13 'irredsol-1.4.tar.gz', or any other archive format suitable for your
35 Please do not hesitate to report any bugs or other problems/suggestions to the
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| /dports/math/gap/gap-4.11.0/pkg/primgrp-3.4.0/lib/ |
| H A D | irredsol.gd | 9 ## This file contains the functions and data for the irreducible solvable
11 ## 372 conjugacy classes of irreducible solvable subgroups of $GL(n,p)$
32 ## A JS-maximal is a maximal irreducible solvable subgroup of
87 ## function does not guarantee any ordering of the groups in the database.
109 ## of irreducible solvable subgroup of GL(<A>n</A>, <A>p</A>),
145 ## irreducible solvable subgroup of
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| /dports/math/py-sympy/sympy-1.9/doc/src/modules/polys/ |
| H A D | basics.rst | 64 any commutative ring `A`, and the corresponding polynomial ring
194 The irreducible elements in the ring of integers are the prime numbers
196 invertible and there are no irreducible elements.
202 any two such products have the same number of irreducible factors
207 more generally polynomial rings over any factorial domain. Fields
208 are trivially factorial since there are only units. The irreducible
370 If `f = cp` is irreducible in `\mathbb{Z}[x]`, then either `c` or `p`
371 must be a unit. If `p` is not a unit, it must be irreducible also in
377 ii. primitive polynomials that are irreducible in `\mathbb{Q}[x]`.
380 of irreducible elements. It suffices to factor its content and
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| /dports/math/e-antic/flint2-ae7ec89/doc/source/ |
| H A D | fmpz_poly_factor.rst | 88 of `F` into (not necessarily irreducible) factors that themselves
104 does a brute force search for irreducible factors of `F` over the
135 any polynomial `F`, and stores a factorization in ``final_fac``.
149 as input any polynomial `F`, and stores a factorization in
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