1x: user defined variable 2 3sin(x): sine of x. 4 5f = 6 ()->1 7 8echo: default 9 10echo: default 11 12log: default 13 14new is aliased to: 15 16sin(x): sine of x. 17 18test1 19 20test2 21 22test3 23 24test4 25 26new is aliased to: 27 28test2 29 30does_not_exist: unknown identifier 31 32Help topics: for a list of relevant subtopics, type ?n for n in 33 0: user-defined functions (aliases, installed and user functions) 34 1: PROGRAMMING under GP 35 2: Standard monadic or dyadic OPERATORS 36 3: CONVERSIONS and similar elementary functions 37 4: functions related to COMBINATORICS 38 5: NUMBER THEORETICAL functions 39 6: POLYNOMIALS and power series 40 7: Vectors, matrices, LINEAR ALGEBRA and sets 41 8: TRANSCENDENTAL functions 42 9: SUMS, products, integrals and similar functions 43 10: General NUMBER FIELDS 44 11: Associative and central simple ALGEBRAS 45 12: ELLIPTIC CURVES 46 13: L-FUNCTIONS 47 14: MODULAR FORMS 48 15: MODULAR SYMBOLS 49 16: GRAPHIC functions 50 17: The PARI community 51Also: 52 ? functionname (short on-line help) 53 ?\ (keyboard shortcuts) 54 ?. (member functions) 55Extended help (if available): 56 ?? (opens the full user's manual in a dvi previewer) 57 ?? tutorial / refcard / libpari (tutorial/reference card/libpari manual) 58 ?? refcard-ell (or -lfun/-mf/-nf: specialized reference card) 59 ?? keyword (long help text about "keyword" from the user's manual) 60 ??? keyword (a propos: list of related functions). 61Member functions, followed by relevant objects 62 63a1-a6, b2-b8, c4-c6 : coeff. of the curve. ell 64area : area ell 65bid : big ideal bid, bnr 66bnf : big number field bnf,bnr 67clgp : class group bid, bnf,bnr 68cyc : cyclic decomposition (SNF) bid, clgp,ell, bnf,bnr 69diff, codiff: different and codifferent nf,bnf,bnr 70disc : discriminant ell,nf,bnf,bnr,rnf 71e, f : inertia/residue degree prid 72fu : fundamental units bnf 73gen : generators bid,prid,clgp,ell, bnf,bnr, gal 74group: group ell, gal 75index: index nf,bnf,bnr 76j : j-invariant ell 77mod : modulus bid, bnr, gal 78nf : number field nf,bnf,bnr,rnf 79no : number of elements bid, clgp,ell, bnf,bnr 80omega, eta: [w1,w2] and [eta1, eta2] ell 81orders: relative orders of generators gal 82p : rational prime prid, ell,nf,bnr,bnr,rnf,gal 83pol : defining polynomial nf,bnf,bnr, gal 84polabs: defining polynomial over Q rnf 85reg : regulator bnf 86roots: roots ell,nf,bnf,bnr, gal 87sign,r1,r2 : signature nf,bnf,bnr 88t2 : t2 matrix nf,bnf,bnr 89tate : Tate's [u^2, u, q, [a,b], L, Ei] ell 90tu : torsion unit and its order bnf 91zk : integral basis nf,bnf,bnr,rnf 92zkst : structure of (Z_K/m)* bid, bnr 93 94# : enable/disable timer 95## : print time for last result 96\\ : comment up to end of line 97\a {n} : print result in raw format (readable by PARI) 98\B {n} : print result in beautified format 99\c : list all commands (same effect as ?*) 100\d : print all defaults 101\e {n} : enable/disable echo (set echo=n) 102\g {n} : set debugging level 103\gf{n} : set file debugging level 104\gm{n} : set memory debugging level 105\h {m-n}: hashtable information 106\l {f} : enable/disable logfile (set logfile=f) 107\m {n} : print result in prettymatrix format 108\o {n} : set output method (0=raw, 1=prettymatrix, 2=prettyprint, 3=2-dim) 109\p {n} : change real precision 110\pb{n} : change real bit precision 111\ps{n} : change series precision 112\q : quit completely this GP session 113\r {f} : read in a file 114\s : print stack information 115\t : print the list of PARI types 116\u : print the list of user-defined functions 117\um : print the list of user-defined member functions 118\v : print current version of GP 119\w {nf} : write to a file 120\x {n} : print complete inner structure of result 121\y {n} : disable/enable automatic simplification (set simplify=n) 122 123{f}=optional filename. {n}=optional integer 124 125 126cmp divrem lex max min shift shiftmul sign 127vecmax vecmin 128 129test6 130 131List of the PARI types: 132 t_INT : long integers [ cod1 ] [ cod2 ] [ man_1 ] ... [ man_k ] 133 t_REAL : long real numbers [ cod1 ] [ cod2 ] [ man_1 ] ... [ man_k ] 134 t_INTMOD : integermods [ code ] [ mod ] [ integer ] 135 t_FRAC : irred. rationals [ code ] [ num. ] [ den. ] 136 t_FFELT : finite field elt. [ code ] [ cod2 ] [ elt ] [ mod ] [ p ] 137 t_COMPLEX: complex numbers [ code ] [ real ] [ imag ] 138 t_PADIC : p-adic numbers [ cod1 ] [ cod2 ] [ p ] [ p^r ] [ int ] 139 t_QUAD : quadratic numbers [ cod1 ] [ mod ] [ real ] [ imag ] 140 t_POLMOD : poly mod [ code ] [ mod ] [ polynomial ] 141 ------------------------------------------------------------- 142 t_POL : polynomials [ cod1 ] [ cod2 ] [ man_1 ] ... [ man_k ] 143 t_SER : power series [ cod1 ] [ cod2 ] [ man_1 ] ... [ man_k ] 144 t_RFRAC : irred. rat. func. [ code ] [ num. ] [ den. ] 145 t_QFR : real qfb [ code ] [ a ] [ b ] [ c ] [ del ] 146 t_QFI : imaginary qfb [ code ] [ a ] [ b ] [ c ] 147 t_VEC : row vector [ code ] [ x_1 ] ... [ x_k ] 148 t_COL : column vector [ code ] [ x_1 ] ... [ x_k ] 149 t_MAT : matrix [ code ] [ col_1 ] ... [ col_k ] 150 t_LIST : list [ cod1 ] [ cod2 ][ vec ] 151 t_STR : string [ code ] [ man_1 ] ... [ man_k ] 152 t_VECSMALL: vec. small ints [ code ] [ x_1 ] ... [ x_k ] 153 t_CLOSURE: functions [ code ] [ arity ] [ code ] [ operand ] [ data ] [ te 154xt ] 155 t_ERROR : error context [ code ] [ errnum ] [ dat_1 ] ... [ dat_k ] 156 t_INFINITY: a*infinity [ code ] [ a ] 157 158f = 159 ()->1 160 161g = 162 ()->0 163 164a&&b: boolean operator "and". 165 166x==y: return 1 if x and y are equal, 0 otherwise. 167 168Total time spent: 0 169