# Index

Symbols | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Z

## Symbols

 < <=, [1] <> = ==, [1] >=, [1] ? @interact

## B

 Basic Arithmetic Basic Arithmetic and Functions BCH Codes BCHCode bitbucket bool Booleans

## C

 Calculus Commands cardinality Cartesian product cayley_table CC ceil ceiling center characteristic characteristic_polynomial check_mat Chinese Remainder Theorem Coding Theory check matrix generating matrix hamming distance hamming weight minimum distance coefficients Coercion explicit implicit column columns, [1] command line concatenation of strings conditionals Contributing to the tutorial contribution cos count crt Cyclic Codes CyclicCode CyclicPermutationGroup, [1]

## D

 decimal approximation Declaring Variables decode def defining mathematical functions degree del derivative Derivatives partial det diagonal DiCyclicGroup dimension direct product divides division, [1] Division and factoring divisors, [1] divmod, [1] dual_code

## E

 e echelon_form echelonize eigenvectors_right elif elimination_ideal else equations euclidean algorithm exp exponential function exponentiation exponents extend extended_code external files external programs gap singular

## F

 factor, [1], [2], [3], [4] factoring False, [1] Field Extensions generating polynomial modulus find_root Finding critical points floor for for statement fractional powers functions arguments definition multiple arguments return values

## G

 gcd, [1], [2], [3] gen_mat gen_mat_systematic gens, [1] gens_small Getting Started GF, [1] Graphics adding two plots aspect_ratio color greatest common divisor groebner_basis groups Cayley table Klein 4 alternating cyclic cyclic; DihedralGroup dihedral generators homomorphisms kernel of homomorphism order permutation subgroup

## H

 Hamming Codes hamming_weight HammingCode help DESCRIPTION EXAMPLES INPUT command line How to use this tutorial hyperbolic trigonometric functions

## I

 ideal Ideals construction gens membership Idempotent Polynomials identity_matrix, [1] if statement if-else statement in, [1] Indeterminants index inequalities integers Integers, [1] integral Integrals definate indefinite interact interactive applets intersection inverse, [1] inverse trigonometric functions is_abelian is_cyclic is_field, [1] is_idempotent is_integral_domain, [1] is_invertible is_irreducible, [1] is_prime, [1] is_primitive is_principal is_ring is_subgroup is_unit, [1]

## J

 joining strings Jordan Canonical Form jordan_form

 kernel

## L

 lc lcm least common multiple left_kernel len, [1] length lexicographic monomial ordering limit Limits directional Line tangent to a curve linear algebra Linear Codes dimension length linear congruences LinearCode linestyle list, [1] append comprehensions concatenation count definition extend index length remove slice sort zip lists map lm ln load load_session loading a file log logarithms loops for while lt

## M

 map, [1] matrix, [1] column determinant diagonal invertability manipulation row rows matrix arithmetic matrix_from_columns matrix_from_rows matrix_from_rows_and_columns MatrixSpace max maximum mean median min Mini-Topic Idempotent Polynomials minimum minimum_distance mod mode modular arithmetic modulus Monomial Orderings monomials moving_average multiplication multiplicative_order, [1] Multivariate Polynomial Division Algorithm Multivariate Polynomial Rings monomials

## N

 n natural base normal coset; conjugation; quotient; homomorphism not notebook nth root number fields

## O

 Objects or order, [1], [2] additive multiplicative Order of operations

## P

 parametric_plot parent, [1], [2], [3], [4], [5] PermutationGroup PermutationGroupMorphism plot parametric plot3d Plotting 2D 3D aspect_ratio polar polar_plot polynomial Polynomial Arithmetic Polynomial Rings gcd xgcd PolynomialRing, [1], [2], [3], [4] prime prime_divisors prod, [1] Programming in Sage Properties of Rings punctured

## Q

 QQ quotient, [1], [2] Quotient Rings qutient

## R

 random rank Reduction modulo an ideal remainder remove rescale_col rescale_row reset restore, [1] reStructured Text return right_kernel rings integers modulo n list order size unit group units Rings characteristic roots row row_space rows RR

## S

 Sage as a Calculator save_session sessions Set cardinality difference intersection subsets symmetric difference union set difference set_block set_column set_row show sign sin sinh slices solve solve_mod solve_right solving equations Solving equations and inequalities Solving equations with several variables Solving for x sort source code ?? split, [1] sqrt square root standard deviation Standard functions and constants Statistics std string strings concatenation join len split subgroup subgroups subsets subtraction sum swap_columns swap_rows symbolic variables symmetric difference SymmetricGroup

## T

 tab completion Tab-completion tan terms thickness total_degree transpose, [1], [2] trigonometric functions True, [1] tutorial source

## U

 union unit group unit_gens unit_group_order Universes Universes and coercion

## V

 var, [1] variables deleting reset restore Variables assignment symbolic variance vector, [1] Vector and Matrix Spaces

## W

 weight_distribution weight_enumerator while statement

## X

 xgcd, [1]

## Z

 zero_matrix zip ZZ