All functions of Erable| listed in alphabetic order

The following symbols will be used:

• %: real
• C%: complex
• n: integer (real integer)
• [ ]: numeric array
• { l }: list
• { m }: symbolic array
• p: polynomial ({ p } for a list-polynomial),
• { v }: list of variables
• s: symbolic object
• v: variable (global name or irrational symbolic)
• f: a fraction
• N, D: numerator and denominator of a fraction
• o: object

List of all global variables in HOME, algb or algbg:

Name	Function	Arguments	Returns
EPS	$\varepsilon$		%
ERABLMSG	Risch log		string
INVLAP	Last inverse Laplace	nothing	s
MATRIX	Last matrix	nothing	m
MODULO	Arithmetic in $Z\!\!Z/nZ\!\!Z$		n
ODETYPE	Ordinary diff. equ. type		string
PRIMIT	Last primitive	nothing	s
SYSTEM	Last system	nothing	$\{ m v \}$
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

If you are short in memory, you can erase all variables in { 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 $\leftrightarrow$ list	[ ] ou { m }	{ m } or [ ]
AXQ	array to s quadratic form	{ m }	s
		2: { m }, 1: { v }	s
C2P	Cycles $\rightarrow$ permutation	{ cycles }	p
CHS	Change signe	o	-o
COLC	Factorization	s	s
COSN	$\cos, \sin(nx) \rightarrow P(\cos x, \sin x)$	n > 0	2: s, 1: s
		n<0	2: { p }, 1: { p }
CIRC	Compose 2 permutations	2:p2, 1:p1	$p_2\circ p_1$
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	$\varphi (n)$
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 $\exp, \ln$	s	s
EXPLIN	Linearization of $\exp$	s	s
FACTO	Factorization	o	3: { v } 2: f , 1: { f1 n1 f2 n2 ... }
FCOEF	roots/poles $\rightarrow$ 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	$n \times n$ 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	$\int _a^b f(t) \ dt$, u	$[uv]_a^b-\int _a^b u v'(t) dt$ (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 }	$\Delta f$
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: $r \times c$ 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	`` $o_2 \times o_1$''
MULT	product	2: o2, o1	$o_2 \times o_1$
NDXF	create a fraction	2: N, 1: D	f=N/D
ORND	Round an object	2: o, 1: D	o

P2C	Permutation $\rightarrow$ cycles	p	3: p, 2: cycles, 1: signature
PCAR	Characteristic polynomial	endomorphism	s
PF	Partial fraction	f	$\sum_i f_i$
PFEXEC	exec between + and -	2: $\sum_i f_i$ 1: prg	$\sum_i \mbox{prg}(f_i)$
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'' $\times$ of matrices	M, M'	``$M \dot M'$ ''
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$2\theta$
TCHEB	Polynomials	integer r	list of r+1 polynomials
TEXPA	Expand transcendent functions	s	s
TNBA	Tangent, normal, ...	$\{ v \}$
TR	trace	[ ] or { m } $=(a_{ij})_{1\leq i,j\leq n}$	$\sum _{i=1}^{n} a_{ii}$
TRAN	transposed	[ ] or { m }	[ ] ou { m }
TRIG	Trigonometry: $\rightarrow \sin, \cos, \arctan$	s	s
TRIGCOS	Trigonometry: $\sin^2 \rightarrow 1-\cos^2$	s	s
TRIGLIN	Trig. linearization	C%, s ou { p }	s
TRIGSIN	Trigonometry: $\sin^2 \rightarrow 1-\cos^2$	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	$\rightarrow$ Numeric	o	o
XQ	$\rightarrow$ 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	$\overline{o}$
cross	Wedge product	2: x, 1: y	$x \wedge y$
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	$\Im (o)$
re	real part	o	$\Re(o)$
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	$(n_1+n_2) \mbox{ mod } n$
MODSUBT	Modular subtraction	2: n1, 1:n2	$(n_1-n_2) \mbox{ mod } n$
MODMULT	Modular multiplicatin	2: n1, 1:n2	$(n_1*n_2) \mbox{ mod } n$
MODDIV	Modular division	2: n1, 1:n2	$(n_1/n_2) \mbox{ mod } n$
MODPOW	Modular power	2: n1, 1:n2	$n_1^{n_2} \mbox{ mod } n$
MODINV	Modular inversion	1: n1	$n_1^{-1} \mbox{ mod } n$
PA2B2	Prime factorization	1: p ( $p\equiv 1[4]$)	1: a+ib/ a2+b2=p