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Release calc version 2.11.0t10

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Landon Curt Noll
1999-11-11 05:15:39 -08:00
parent 86c8e6dcf1
commit 96c34adee3
283 changed files with 2380 additions and 3032 deletions
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26
lib/poly.cal
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@@ -1,6 +1,6 @@
/*
* A collection of functions designed for calculations involving
* polynomials in one variable (by Ernest W. Bowen).
* polynomials in one variable (by Ernest W. Bowen).
*
* On starting the program the independent variable has identifier x
* and name "x", i.e. the user can refer to it as x, the
@@ -24,25 +24,25 @@
* would assign to q a number value. As with number expressions
* involving operations, the expression used to define the
* polynomial is usually lost; in the above example, the normal
* computer display for p will be x^2 - 2x + 1. Different
* computer display for p will be x^2 - 2x + 1. Different
* identifiers may of course have the same polynomial value.
*
* The polynomial we think of as a_0 + a_1 * x + ... + a_n * x^n,
* for number coefficients a_0, a_1, ... a_n may also be
* constructed as pol(a_0, a_1, ..., a_n). Note that here the
* constructed as pol(a_0, a_1, ..., a_n). Note that here the
* coefficients are to be in ascending power order. The independent
* variable is pol(0,1), so to use t, say, as an identifier for
* this, one may assign t = pol(0,1). To simultaneously specify
* an identifier and a name for the independent variable, there is
* the instruction var, used as in identifier = var(name). For
* the instruction var, used as in identifier = var(name). For
* example, to use "t" in the way "x" is initially, one may give
* the instruction t = var("t").
* the instruction t = var("t").
*
* There are four parameters pmode, order, iod and ims for controlling
* the format in which polynomials are displayed.
* The parameter pmode may have values "alg" or "list": the
* former gives a display as an algebraic formula, while
* the latter only lists the coefficients. Whether the terms or
* the latter only lists the coefficients. Whether the terms or
* coefficients are in ascending or descending power order is
* controlled by order being "up" or "down". If the
* parameter iod (for integer-only display), the polynomial
@@ -69,7 +69,7 @@
* polynomial, list or matrix were a function. For example,
* if a = 1 + x^2, a(2) will return the value 5, just as if
* define a(t) = 1 + t^2;
* had been used. However, when the polynomial definition is
* had been used. However, when the polynomial definition is
* used, changing the polynomial a will change a(t) to the value
* of the new polynomial at t. For example,
* after
@@ -87,7 +87,7 @@
* Matrices with polynomial elements may be added, subtracted and
* multiplied as long as the usual rules for compatibility are
* observed. Also, matrices may be multiplied by polynomials,
* i.e. if p is a polynomial and A a matrix whose elements
* i.e. if p is a polynomial and A a matrix whose elements
* may be numbers or polynomials, p * A returns the matrix of
* the same shape as A with each element multiplied by p.
* Square matrices may also be 'substituted for the variable' in
@@ -106,7 +106,7 @@
* Functions defined include:
*
* monic(a) returns the monic multiple of a, i.e., if a != 0,
* the multiple of a with leading coefficient 1
* the multiple of a with leading coefficient 1
* conj(a) returns the complex conjugate of a
* ispmult(a,b) returns 1 or 0 according as a is or is not
* a polynomial multiple of b
@@ -119,7 +119,7 @@
* by Newtonian divided difference interpolation, where
* X is a list of x-values, Y a list of corresponding
* y-values. If t is omitted, the interpolating
* polynomial is returned. A y-value may be replaced by
* polynomial is returned. A y-value may be replaced by
* list (y, y_1, y_2, ...), where y_1, y_2, ... are
* the reduced derivatives at the corresponding x;
* i.e. y_r is the r-th derivative divided by fact(r).
@@ -328,7 +328,7 @@ define poly_cmp(a,b) {
local sa, sb;
sa = findlist(a);
sb=findlist(b);
return (sa != sb);
return (sa != sb);
}
define poly_mul(a,b) {
@@ -547,7 +547,7 @@ define D(a, n) {
local i,j,v;
if (isnull(n)) n = 1;
if (!isint(n) || n < 1) quit "Bad order for derivative";
if (ismat(a)) {
if (ismat(a)) {
v = a;
for (i = matmin(a,1); i <= matmax(a,1); i++)
for (j = matmin(a,2); j <= matmax(a,2); j++)
@@ -561,7 +561,7 @@ define D(a, n) {
define Dp(a,n) {
local i, v;
if (n > 1) return Dp(Dp(a, n-1), 1);
obj poly v;
obj poly v;
v.p=list();
for (i=1; i<size(a.p); i++) append (v.p, i*a.p[[i]]);
return v;