## [Maxima-commits] CVS: maxima/doc/info Number.texi,1.5,1.6

 [Maxima-commits] CVS: maxima/doc/info Number.texi,1.5,1.6 From: Robert Dodier - 2004-12-29 07:53:30 ```Update of /cvsroot/maxima/maxima/doc/info In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv16443 Modified Files: Number.texi Log Message: Strike out obsolete, commented-out @node and @unnumberedsec tags in preparation for further editing. Index: Number.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Number.texi,v retrieving revision 1.5 retrieving revision 1.6 diff -u -d -r1.5 -r1.6 --- Number.texi 6 Nov 2004 05:49:56 -0000 1.5 +++ Number.texi 29 Dec 2004 07:53:21 -0000 1.6 @@ -5,23 +5,20 @@ @node Definitions for Number Theory, , Number Theory, Number Theory @section Definitions for Number Theory -@... @node BERN -@... @unnumberedsec phony + @defun BERN (x) gives the Xth Bernoulli number for integer X. ZEROBERN[TRUE] if set to FALSE excludes the zero BERNOULLI numbers. (See also BURN). @end defun -@... @node BERNPOLY -@... @unnumberedsec phony + @defun BERNPOLY (v, n) generates the nth Bernoulli polynomial in the variable v. @end defun -@... @node BFZETA -@... @unnumberedsec phony + @defun BFZETA (exp,n) BFLOAT version of the Riemann Zeta function. The 2nd argument is how many digits to retain and return, it's a good idea to @@ -29,8 +26,7 @@ LOAD(BFFAC); . @end defun -@... @node BGZETA -@... @unnumberedsec phony + @defun BGZETA (S, FPPREC) BGZETA is like BZETA, but avoids arithmetic overflow errors on large arguments, is faster on medium size arguments @@ -39,8 +35,7 @@ LOAD(BFAC);. @end defun -@... @node BHZETA -@... @unnumberedsec phony + @defun BHZETA (S,H,FPPREC) gives FPPREC digits of @example @@ -49,8 +44,7 @@ This is available by doing LOAD(BFFAC);. @end defun -@... @node BINOMIAL -@... @unnumberedsec phony + @defun BINOMIAL (X, Y) the binomial coefficient X*(X-1)*...*(X-Y+1)/Y!. If X and Y are integers, then the numerical value of the binomial @@ -58,8 +52,7 @@ binomial coefficient is expressed as a polynomial. @end defun -@... @node BURN -@... @unnumberedsec phony + @defun BURN (N) is like BERN(N), but without computing all of the uncomputed Bernoullis of smaller index. So BURN works efficiently for large, @@ -73,14 +66,12 @@ approximated by (transcendental) zetas with tolerable efficiency. @end defun -@... @node BZETA -@... @unnumberedsec phony + @defun BZETA - This function is obsolete, see BFZETA. @end defun -@... @node CF -@... @unnumberedsec phony + @defun CF (exp) converts exp into a continued fraction. exp is an expression composed of arithmetic operators and lists which represent continued @@ -92,8 +83,7 @@ (CF binds LISTARITH to FALSE so that it may carry out its function.) @end defun -@... @node CFDISREP -@... @unnumberedsec phony + @defun CFDISREP (list) converts the continued fraction represented by list into general representation. @@ -112,8 +102,7 @@ @end example @end defun -@... @node CFEXPAND -@... @unnumberedsec phony + @defun CFEXPAND (x) gives a matrix of the numerators and denominators of the next-to-last and last convergents of the continued fraction x. @@ -130,16 +119,14 @@ @end example @end defun -@... @node CFLENGTH -@... @unnumberedsec phony + @defvar CFLENGTH default: [1] controls the number of terms of the continued fraction the function CF will give, as the value CFLENGTH[1] times the period. Thus the default is to give one period. @end defvar -@... @node CGAMMA -@... @unnumberedsec phony + @defun CGAMMA - The Gamma function in the complex plane. Do LOAD(CGAMMA) to use these functions. Functions Cgamma, Cgamma2, and LogCgamma2. @@ -159,44 +146,38 @@ calculated. These two functions are somewhat more efficient. @end defun -@... @node CGAMMA2 -@... @unnumberedsec phony + @defun CGAMMA2 - See CGAMMA. @end defun -@... @node DIVSUM -@... @unnumberedsec phony + @defun DIVSUM (n,k) adds up all the factors of n raised to the kth power. If only one argument is given then k is assumed to be 1. @end defun -@... @node EULER -@... @unnumberedsec phony + @defun EULER (X) gives the Xth Euler number for integer X. For the Euler-Mascheroni constant, see %GAMMA. @end defun -@... @node FACTORIAL -@... @unnumberedsec phony + @defun FACTORIAL (X) The factorial function. FACTORIAL(X) = X! . See also MINFACTORIAL and FACTCOMB. The factorial operator is !, and the double factorial operator is !!. @end defun -@... @node FIB -@... @unnumberedsec phony + @defun FIB (X) the Xth Fibonacci number with FIB(0)=0, FIB(1)=1, and FIB(-N)=(-1)^(N+1) *FIB(N). PREVFIB is FIB(X-1), the Fibonacci number preceding the last one computed. @end defun -@... @node FIBTOPHI -@... @unnumberedsec phony + @defun FIBTOPHI (exp) converts FIB(n) to its closed form definition. This involves the constant %PHI (= (SQRT(5)+1)/2 = 1.618033989). @@ -204,35 +185,30 @@ About %PHI do TELLRAT(%PHI^2-%PHI-1)\$ ALGEBRAIC:TRUE\$ . @end defun -@... @node INRT -@... @unnumberedsec phony + @defun INRT (X,n) takes two integer arguments, X and n, and returns the integer nth root of the absolute value of X. @end defun -@... @node JACOBI -@... @unnumberedsec phony + @defun JACOBI (p,q) is the Jacobi symbol of p and q. @end defun -@... @node LCM -@... @unnumberedsec phony + @defun LCM (exp1,exp2,...) returns the Least Common Multiple of its arguments. Do LOAD(FUNCTS); to access this function. @end defun -@... @node MAXPRIME -@... @unnumberedsec phony + @defvar MAXPRIME default: [489318] - the largest number which may be given to the PRIME(n) command, which returns the nth prime. @end defvar -@... @node MINFACTORIAL -@... @unnumberedsec phony + @defun MINFACTORIAL (exp) examines exp for occurrences of two factorials which differ by an integer. It then turns one into a polynomial times @@ -251,8 +227,7 @@ @end example @end defun -@... @node PARTFRAC -@... @unnumberedsec phony + @defun PARTFRAC (exp, var) expands the expression exp in partial fractions with respect to the main variable, var. PARTFRAC does a complete @@ -263,8 +238,7 @@ the expansion falls out. See EXAMPLE(PARTFRAC); for examples. @end defun -@... @node PRIME -@... @unnumberedsec phony + @defun PRIME (n) gives the nth prime. MAXPRIME[489318] is the largest number accepted as argument. Note: The PRIME command does not work in @@ -272,14 +246,12 @@ do not want. PRIMEP does work however. @end defun -@... @node PRIMEP -@... @unnumberedsec phony + @defun PRIMEP (n) returns TRUE if n is a prime, FALSE if not. @end defun -@... @node QUNIT -@... @unnumberedsec phony + @defun QUNIT (n) gives the principal unit of the real quadratic number field SQRT(n) where n is an integer, i.e. the element whose norm is unity. @@ -293,29 +265,25 @@ @end example @end defun -@... @node TOTIENT -@... @unnumberedsec phony + @defun TOTIENT (n) is the number of integers less than or equal to n which are relatively prime to n. @end defun -@... @node ZEROBERN -@... @unnumberedsec phony + @defvar ZEROBERN default: [TRUE] - if set to FALSE excludes the zero BERNOULLI numbers. (See the BERN function.) @end defvar -@... @node ZETA -@... @unnumberedsec phony + @defun ZETA (X) gives the Riemann zeta function for certain integer values of X. @end defun -@... @node ZETA%PI -@... @unnumberedsec phony + @defvar ZETA%PI default: [TRUE] - if FALSE, suppresses ZETA(n) giving coeff*%PI^n for n even. ```

 [Maxima-commits] CVS: maxima/doc/info Number.texi,1.5,1.6 From: Robert Dodier - 2004-12-29 07:53:30 ```Update of /cvsroot/maxima/maxima/doc/info In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv16443 Modified Files: Number.texi Log Message: Strike out obsolete, commented-out @node and @unnumberedsec tags in preparation for further editing. Index: Number.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Number.texi,v retrieving revision 1.5 retrieving revision 1.6 diff -u -d -r1.5 -r1.6 --- Number.texi 6 Nov 2004 05:49:56 -0000 1.5 +++ Number.texi 29 Dec 2004 07:53:21 -0000 1.6 @@ -5,23 +5,20 @@ @node Definitions for Number Theory, , Number Theory, Number Theory @section Definitions for Number Theory -@... @node BERN -@... @unnumberedsec phony + @defun BERN (x) gives the Xth Bernoulli number for integer X. ZEROBERN[TRUE] if set to FALSE excludes the zero BERNOULLI numbers. (See also BURN). @end defun -@... @node BERNPOLY -@... @unnumberedsec phony + @defun BERNPOLY (v, n) generates the nth Bernoulli polynomial in the variable v. @end defun -@... @node BFZETA -@... @unnumberedsec phony + @defun BFZETA (exp,n) BFLOAT version of the Riemann Zeta function. The 2nd argument is how many digits to retain and return, it's a good idea to @@ -29,8 +26,7 @@ LOAD(BFFAC); . @end defun -@... @node BGZETA -@... @unnumberedsec phony + @defun BGZETA (S, FPPREC) BGZETA is like BZETA, but avoids arithmetic overflow errors on large arguments, is faster on medium size arguments @@ -39,8 +35,7 @@ LOAD(BFAC);. @end defun -@... @node BHZETA -@... @unnumberedsec phony + @defun BHZETA (S,H,FPPREC) gives FPPREC digits of @example @@ -49,8 +44,7 @@ This is available by doing LOAD(BFFAC);. @end defun -@... @node BINOMIAL -@... @unnumberedsec phony + @defun BINOMIAL (X, Y) the binomial coefficient X*(X-1)*...*(X-Y+1)/Y!. If X and Y are integers, then the numerical value of the binomial @@ -58,8 +52,7 @@ binomial coefficient is expressed as a polynomial. @end defun -@... @node BURN -@... @unnumberedsec phony + @defun BURN (N) is like BERN(N), but without computing all of the uncomputed Bernoullis of smaller index. So BURN works efficiently for large, @@ -73,14 +66,12 @@ approximated by (transcendental) zetas with tolerable efficiency. @end defun -@... @node BZETA -@... @unnumberedsec phony + @defun BZETA - This function is obsolete, see BFZETA. @end defun -@... @node CF -@... @unnumberedsec phony + @defun CF (exp) converts exp into a continued fraction. exp is an expression composed of arithmetic operators and lists which represent continued @@ -92,8 +83,7 @@ (CF binds LISTARITH to FALSE so that it may carry out its function.) @end defun -@... @node CFDISREP -@... @unnumberedsec phony + @defun CFDISREP (list) converts the continued fraction represented by list into general representation. @@ -112,8 +102,7 @@ @end example @end defun -@... @node CFEXPAND -@... @unnumberedsec phony + @defun CFEXPAND (x) gives a matrix of the numerators and denominators of the next-to-last and last convergents of the continued fraction x. @@ -130,16 +119,14 @@ @end example @end defun -@... @node CFLENGTH -@... @unnumberedsec phony + @defvar CFLENGTH default: [1] controls the number of terms of the continued fraction the function CF will give, as the value CFLENGTH[1] times the period. Thus the default is to give one period. @end defvar -@... @node CGAMMA -@... @unnumberedsec phony + @defun CGAMMA - The Gamma function in the complex plane. Do LOAD(CGAMMA) to use these functions. Functions Cgamma, Cgamma2, and LogCgamma2. @@ -159,44 +146,38 @@ calculated. These two functions are somewhat more efficient. @end defun -@... @node CGAMMA2 -@... @unnumberedsec phony + @defun CGAMMA2 - See CGAMMA. @end defun -@... @node DIVSUM -@... @unnumberedsec phony + @defun DIVSUM (n,k) adds up all the factors of n raised to the kth power. If only one argument is given then k is assumed to be 1. @end defun -@... @node EULER -@... @unnumberedsec phony + @defun EULER (X) gives the Xth Euler number for integer X. For the Euler-Mascheroni constant, see %GAMMA. @end defun -@... @node FACTORIAL -@... @unnumberedsec phony + @defun FACTORIAL (X) The factorial function. FACTORIAL(X) = X! . See also MINFACTORIAL and FACTCOMB. The factorial operator is !, and the double factorial operator is !!. @end defun -@... @node FIB -@... @unnumberedsec phony + @defun FIB (X) the Xth Fibonacci number with FIB(0)=0, FIB(1)=1, and FIB(-N)=(-1)^(N+1) *FIB(N). PREVFIB is FIB(X-1), the Fibonacci number preceding the last one computed. @end defun -@... @node FIBTOPHI -@... @unnumberedsec phony + @defun FIBTOPHI (exp) converts FIB(n) to its closed form definition. This involves the constant %PHI (= (SQRT(5)+1)/2 = 1.618033989). @@ -204,35 +185,30 @@ About %PHI do TELLRAT(%PHI^2-%PHI-1)\$ ALGEBRAIC:TRUE\$ . @end defun -@... @node INRT -@... @unnumberedsec phony + @defun INRT (X,n) takes two integer arguments, X and n, and returns the integer nth root of the absolute value of X. @end defun -@... @node JACOBI -@... @unnumberedsec phony + @defun JACOBI (p,q) is the Jacobi symbol of p and q. @end defun -@... @node LCM -@... @unnumberedsec phony + @defun LCM (exp1,exp2,...) returns the Least Common Multiple of its arguments. Do LOAD(FUNCTS); to access this function. @end defun -@... @node MAXPRIME -@... @unnumberedsec phony + @defvar MAXPRIME default: [489318] - the largest number which may be given to the PRIME(n) command, which returns the nth prime. @end defvar -@... @node MINFACTORIAL -@... @unnumberedsec phony + @defun MINFACTORIAL (exp) examines exp for occurrences of two factorials which differ by an integer. It then turns one into a polynomial times @@ -251,8 +227,7 @@ @end example @end defun -@... @node PARTFRAC -@... @unnumberedsec phony + @defun PARTFRAC (exp, var) expands the expression exp in partial fractions with respect to the main variable, var. PARTFRAC does a complete @@ -263,8 +238,7 @@ the expansion falls out. See EXAMPLE(PARTFRAC); for examples. @end defun -@... @node PRIME -@... @unnumberedsec phony + @defun PRIME (n) gives the nth prime. MAXPRIME[489318] is the largest number accepted as argument. Note: The PRIME command does not work in @@ -272,14 +246,12 @@ do not want. PRIMEP does work however. @end defun -@... @node PRIMEP -@... @unnumberedsec phony + @defun PRIMEP (n) returns TRUE if n is a prime, FALSE if not. @end defun -@... @node QUNIT -@... @unnumberedsec phony + @defun QUNIT (n) gives the principal unit of the real quadratic number field SQRT(n) where n is an integer, i.e. the element whose norm is unity. @@ -293,29 +265,25 @@ @end example @end defun -@... @node TOTIENT -@... @unnumberedsec phony + @defun TOTIENT (n) is the number of integers less than or equal to n which are relatively prime to n. @end defun -@... @node ZEROBERN -@... @unnumberedsec phony + @defvar ZEROBERN default: [TRUE] - if set to FALSE excludes the zero BERNOULLI numbers. (See the BERN function.) @end defvar -@... @node ZETA -@... @unnumberedsec phony + @defun ZETA (X) gives the Riemann zeta function for certain integer values of X. @end defun -@... @node ZETA%PI -@... @unnumberedsec phony + @defvar ZETA%PI default: [TRUE] - if FALSE, suppresses ZETA(n) giving coeff*%PI^n for n even. ```