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The new DERIVE for DOS combines the advantages of the "classic" DERIVE and the DERIVE XM (extended memory version). Its system requirements are simple: any PC compatible computer with 512K memory. If you are running on a 386 or higher processor, with 2 MB or more of extended memory, the software will automatically run in 32-bit mode using extended memory; otherwise it will run in 16-bit mode using 640 KB of memory.
When DERIVE.EXE starts, it automatically switches to 32-bit mode if running on an 80386 or higher processor. If for some reason DERIVE does not work in 32-bit mode on your computer, you can run it in 16-bit mode by executing the program DERIVE16.COM.
Finite sets can be entered using braces (e.g. {1, 2, 3} ). Ellipses can be used to enter a sequence of elements of sets or vectors (e.g. {1, ..., 10} or [0, 2, ..., 10] ). The following set operators and functions are built-in:
s UNION t simplifies to the union of s and t.
s INTERSECTION t simplifies to the intersection of s and t.
s \ t simplifies to the set difference of s and t (i.e. those elements of s not in t). For example, {1,...,10}\{2,3,5,7} simplifies to {1,4,6,8,9,10}.
s` simplifies to the set complement of s. For example, s`` simplifies to s.
POWER_SET(s) simplifies to all the subsets of s. POWER_SET(s,n) simplifies to all the subsets of s having exactly n elements.
Note that sets can be simplified algebraically (e.g. s INTERSECTION s` simplifies to the empty set {} ).
If F has been declared an arbitrary function (see Section 4.12), then DIF(F(u),u) can be entered and is displayed as F'(u). For example, DIF(F(SIN(x)),x) simplifies to COS(x)*F'(SIN(x)).
The following summarizes the new functions defined in the various MTH utility files distributed with DERIVE (see Chapter 9):
PARTITION(v,n,d) in VECTOR.MTH simplifies to a partition of vector v into vectors of length n with an offset delta of d. d defaults to n. For example, PARTITION([1,2,3,4,5],3,2) simplifies to the matrix [[1,2,3],[3,4,5]].
RANDOM_NORMAL(s,m) in MISC.MTH simplifies to a random value with a normal distribution having a standard deviation of s and a mean value of m.
INVERSE_MOD(m,n) in NUMBER.MTH simplifies to the inverse of m mod n. For example, INVERSE_MOD(37,53) simplifies to 43.
SOLVE_MOD(u,x,n) in NUMBER.MTH simplifies to a vector of solutions of the linear congruence equation u(x)=0 mod n. For example, SOLVE_MOD(3*x-30,x,9) simplifies to [1,4,7].
PELL(n) in NUMBER.MTH simplifies to the nth Pell number. For example, PELL(10) simplifies to 985.
LUCAS(n) in NUMBER.MTH simplifies to the nth Lucas number. For example, LUCAS(10) simplifies to 123.
BELL(n) in NUMBER.MTH simplifies to the nth Bell or exponential number. For example, BELL(10) simplifies to 115975.
RECURRENCE(u,v,v0,m) in NUMBER.MTH simplifies to a vector of m elements of the recurrence u where v0 is a vector of the first elements and v is a variable. For example, RECURRENCE(v SUB 1 + v SUB 2,v,[1,1],8) simplifies to [1,1,2,3,5,8,13,21] that is the first 8 Fibonacci numbers.
POLYGONAL_PYRAMID(n,p,d) in NUMBER.MTH simplifies to the nth p-sided dth-dimensional polygonal pyramid number, p>=2. For example, POLYGONAL_PYRAMID(n,3,2), POLYGONAL_PYRAMID(n,3,3), and POLYGONAL_PYRAMID(n,3,4) simplify to the nth triangular, tetrahedral, and pentatope numbers, respectively.
POLYGONAL(n,p) in NUMBER.MTH simplifies to the nth p-sided polygonal number, p>=2. For example POLYGONAL(10,3) simplifies to 55.
CENTERED_PYRAMID(n,p,d) in NUMBER.MTH simplifies to the nth p-sided dth-dimensional centered pyramid number, p>=2. For example, CENTERED_PYRAMID(n,6,2) and CENTERED_PYRAMID(n,4,3) simplify to the nth hex and octahedral numbers, respectively.
CENTERED_CUBE(n,d) and CENTERED_HEX(n,d) in NUMBER.MTH simplify to the nth dth-dimensional centered cube and hex numbers, respectively. For example, CENTERED_HEX(n,3) simplifies to the the nth rhombic dodecahedral number.
PERFECT(n) in NUMBER.MTH simplifies to the nth perfect number (i.e. numbers that are equal to the sum of their divisors). For example, PERFECT(2) simplifies to 28.
In ORTH_POL.MTH new functions for producing the first n orthogonal polynomials are defined using a recurrence.
The USERS directory on the DERIVE diskette includes the following utility packages contributed at no charge by various DERIVE users:
CALLOPTN Call option package for stocks
CURV_FIT Curve fitting package
EULERMAC Euler-Maclaurin summation formula
FIT_ Linear & rational fit to weighted data package
FUN Special mathematical function package
HERMITE Interpolating polynomial package
MAT_3DPL 3D data point and matrices plot package
ODE Exact first and second order ODE package
PSERIES Power series package
ROMB_INT Romberg integration package
SECANT Secant approximation package
SPLINE Cubic spline package
TAY_ODE Approximate first and second order ODE package
TENSOR Tensor algebra and analysis package
Some of the MTH files for these packages are very large. To save space when loading them, use a Transfer Load Utility command rather than a Transfer Load Derive command. Corresponding to each MTH file is a DOC file that documents the package. Some packages also have a DMO file that can be run after the MTH file is loaded. If you have questions about a package, contact the package's author directly. The author's name is given in the package's DOC file.
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