List of all global variables in HOME
, algb
or
algbg
:
Name | Function | Arguments | Returns |
EPS | % | ||
ERABLMSG | Risch log | string | |
INVLAP | Last inverse Laplace | nothing | s |
MATRIX | Last matrix | nothing | m |
MODULO | Arithmetic in | n | |
ODETYPE | Ordinary diff. equ. type | string | |
PRIMIT | Last primitive | nothing | s |
SYSTEM | Last system | nothing | |
GX/SX/UKEYS | User keys string | nothing | string |
VX | integration variable | Rien | v |
fr | French short doc | nothing | string |
us | English short doc | nothing | string |
{ HOME }
and subdirectories except EPS
, VX
and MODULO
.
Functions of the Erable
library and of the other
,
algb
or algbg
directories:
Name | Function | Arguments | Returns |
ABCUV | Bezout ax+by=c | 3,2,1:a, b, c | 1:1 [3,2: x, y] or 1: 0 |
AXL | array list | [ ] ou { m } | { m } or [ ] |
AXQ | array to s quadratic form | { m } | s |
2: { m }, 1: { v } | s | ||
C2P | Cycles permutation | { cycles } | p |
CHS | Change signe | o | -o |
COLC | Factorization | s | s |
COSN | n > 0 | 2: s, 1: s | |
n<0 | 2: { p }, 1: { p } | ||
CIRC | Compose 2 permutations | 2:p2, 1:p1 | |
CURL | Rotationnal | 2: { s1 s2 s3 } 1: { v } | { s1' s2' s3' } |
DEGRE | Order | { p } | n |
DIV | Divergence | 2: { s1 ... sk } 1: { v } | s |
DIV1 | Usual division | 2: o2, 1: o1 | o2/o1 |
DIV2 | Euclidean division | 2: o2, 1: o1 | 2: o2 div o1,1: o2 mod o1 |
DIVIS | List of divisors | o | { l } |
DIVPC | Division in ascending power | 3: s, 2: s', 1: n | s |
DSOLVE | Solve y'(x)=f(y(x),x) | f(y(x),x) | y(x) |
EPSX0 | Strip expression | o | o |
EULER | Euler indicatrix | n | |
EXEC | Substitution or doall | 2: { l }, 1: program | 1: { l } |
2: s, 1: o1=o2 | s | ||
3: s, 2: l1 1: l2 | s | ||
EXPA | Simplification | o | o' |
EXPLN | Conversion to | s | s |
EXPLIN | Linearization of | s | s |
FACTO | Factorization | o | 3: { v } 2: f , 1: { f1 n1 f2 n2 ... } |
FCOEF | roots/poles Fraction | { r1 n1 r2 n2 ... } | f |
FROOTS | Factorization | o | 3: { v } 2: f , 1: { s1 n1 s2 n2 ... } |
FSIGN | Sign of a rational fraction | s | tagged list |
FXND | Split a fraction | f=N/D | 2: N, 1: D |
GAUSS | Gauß quadratic form reduction | 1: A | 2: D, 1: P |
s | 5: D,4: P, 3: A, 2: { v },1: s | ||
2: s, 1: { v } | 5: D,4: P, 3: A, 2: { v },1: s | ||
GCD1 | Greatest common divisor | 2: o2, 1: o1 | GCD(o2,o1) |
GCD3 | GCD (solves au+bv=d) | 2,1: a , b | GCD(a,b)=d, u, v |
HALFTAN | To half angle tangent | ||
HERMITE | Hermite polynomial | integer n | Hn |
HESS | Hessian | 2: s, 1: { v } | matrix |
HILBERT | Hilbert matrix | integer n | matrix |
HORN | Horner scheme | 2:p , 1: r | 3: p/(X-r) , 2: r, 1: P(r) |
ILAP | Inverse laplace transform | s | L-1(s) |
INIT | Initialization | nothing | nothing |
INVL | Inversion | o | o-1 |
IPP | Integration by part | , u | (v=f/u') |
JORDAN | Diagonalization | endomorphism | 7 to 1: cf. section 12 |
KERN | Kernel of a lin. appl. | m | 4 to 1: cf. section 12 |
LAP | Laplace transform | 2:f, 1:g | L(f)/g |
LAPL | Laplacian | 2: f, 1: { v } | |
LATEX | LATEX conversion | 1: s | 1: string |
L2S | Evaluation | 2: { p }, 1:v | p(v) |
2: { p },1: { v } | p(v) | ||
LCM1 | Least common multiple | 2: o2, 1: o1 | LCM(o2,o1) |
LCXM | Matrix creation | 3: r, 2: c, 1: prog | 1: matrix |
LDEC | Lin Diff Equ Cst Coef | 2: { v }, 1: { m } | 3,2: (m-x)-1, 1: (m-x)-1 v |
LEGENDRE | Polynomials | integer r | list of r+1 polynomials |
LGCD | GCD of a list | { l } | o=GCD |
LIDNT | List of variables | s | 2: s, 1: { v } |
LIMIT | Limit | 3:s, 2:v, 1:n | s |
LNCOLC | Collect log | s | s |
LU2 | LU decomposition | M | L-1, U |
LVAR | list of variables | o | { v } |
MAD | inverse, char. polyn., etc. | o | 4: det, 3: 1/o, 2: { p },1: { p } |
MMULT | special product | 3: o2, o1, n | `` '' |
MULT | product | 2: o2, o1 | |
NDXF | create a fraction | 2: N, 1: D | f=N/D |
ORND | Round an object | 2: o, 1: D | o |
P2C | Permutation cycles | p | 3: p, 2: cycles, 1: signature |
PCAR | Characteristic polynomial | endomorphism | s |
PF | Partial fraction | f | |
PFEXEC | exec between + and - | 2: 1: prg | |
POWER | integral power | 2: o, 1: n | on |
PREVAL | Evaluation | 3: primitive, 2,1:bornes | s |
PTAYL | Taylor for polynomials | 2: P(X), 1: o | P(X-o ) |
PURG | Purge algb(g) | nothing | nothing |
QXA | s quadratic form to array | 2: s, 1: { v } | { m } |
s | 2:{ m }, 1: { v } | ||
RANG | Réduction sous-diagonale | { m } | 2: spec. cases, 1:{ m } |
RDET | Determinant (rref) | endomorphism { m } | 2: { m }, 1: determinant |
RISCH | Symbolic integration | s | s |
S2L | Symbolic to list | 2: o, 1: { v } | 2: { v },1:{ p } |
2: o, 1: v | { p } | ||
SCROLL | Scrolls a grob | grob | |
SERIES | Series | 3: s, 2: v, 1: n | 6: 6-1: s |
SETFR | Set French Flags | nothing | nothing |
SIMP2 | Simplification | 2: o2, 1: o1 | 2: o2', 1: o1' |
SINCOS | Exponential to sine/cosine | s | s |
SOLGEN | Solves a linear system | { eqns { v } } | cf. section 12 |
SOLV | Solve | 2: s, 1: x | 2: x, 1: solutions |
SQRT | Square root | n or C% or s | n or C% or s |
STUDMULT | ``students'' of matrices | M, M' | `` '' |
SUBT | Subtraction | 2: o2, 1: o1 | o2-o1 |
SXL | Conversion | Internal [user] | User [internal] |
SYST | Solves a linear system | { eqns { v } } | cf. section 12 |
TAN2SC | Tangent to sin/cos | ||
TAN2SC2 | Tangent to sin/cos | ||
TCHEB | Polynomials | integer r | list of r+1 polynomials |
TEXPA | Expand transcendent functions | s | s |
TNBA | Tangent, normal, ... | ||
TR | trace | [ ] or { m } | |
TRAN | transposed | [ ] or { m } | [ ] ou { m } |
TRIG | Trigonometry: | s | s |
TRIGCOS | Trigonometry: | s | s |
TRIGLIN | Trig. linearization | C%, s ou { p } | s |
TRIGSIN | Trigonometry: | s | s |
TRUNC | Truncate an asymptotic expansion | 2: s, 1: rest s' | s |
TSIMP | Simplification (transcendental) | s | s |
VAND | Vandermonde matrix | list of objects | matrix |
VER | Version | rien | % 2.99 |
XFRC | To quadratic irrational | o | o |
XNUM | Numeric | o | o |
XQ | Rational | o | o |
XY | Scalar product of 2 vectors | 2: x 1: y | x.y |
abs | Absolute value | s | s |
add | Addition | 2: o2, 1: o1 | o2+o1 |
arg | Argument | 1: s | 1: s |
comb | Combinaisons | 2: n, 1: n' | Cn'n |
conj | Conjugate | o | |
cross | Wedge product | 2: x, 1: y | |
der | derivative or gradient | 2: s, 1: v | 1: s |
der1 | derivative | s | s |
det | Determinant (expand) | endomorphism | determinant |
fact | Factorielle | n | n! |
idn | identity | real integer or matrix | identity matrix |
im | imaginary part | o | |
re | real part | o | |
rref | Row reduction | M | { s }, reduced matrix |
tEVAL | Execution time | ..., 1: o | EVAL(o), 1: time |
Functions of the kernel
library. Don't forget to set an integer n
in the variable MODULO
(by default n=2):
Name | Function | Arguments | Returns |
{KERNEL.LIB} |
(0:788 ) |
||
MODADD | Modular addition | 2: n1, 1:n2 | |
MODSUBT | Modular subtraction | 2: n1, 1:n2 | |
MODMULT | Modular multiplicatin | 2: n1, 1:n2 | |
MODDIV | Modular division | 2: n1, 1:n2 | |
MODPOW | Modular power | 2: n1, 1:n2 | |
MODINV | Modular inversion | 1: n1 | |
PA2B2 | Prime factorization | 1: p ( ) | 1: a+ib/ a2+b2=p |