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Miscellaneous Tips

Note that there is a shortcut to STRING(V) by just doing T:=“”+V; However, STRING(V) is faster and uses less RAM.

Indefinite integral has an implicit “+ constant” at the end of the results. In some CAS systems it's mentioned, but in the PRIME, it isn't. Note that this is so the result can be cut and pasted without having to delete the extra text, which is preferred. The constant is eliminated when the limits are provided for the definite integral. Note that the preval() function calculates f(b)-f(a), when called like preval(f,a,b[,var]), which can be used to get the definite integral from the indefinite integral.

When working with trigonometric functions, there are a group of functions that can allow for simplification of terms, or expansion in a particular direction. trigcos() will try to express the expression in terms of cosines, similarly with trigsin, trigtan. Likewise, there are a set of functions to convert between exponents, trig and ln functions. simplify and trigexpand can be useful in such cases too. tcollect() can convert an expression involving powers of trig functions to functions of nx. Note that some of these functions can result in a constant at the end of the expression and if this is an indefinite integral result, then this constant can be thrown away without error. ratnormal() can combine multiple fractions into one simplest irreducible fraction. E.g. Calling integrate( (cos(2*x)^3)*(sin(2*x)^5), x ) results in -(1/16)*cos(2*x)^3-(1/6)*cos(2*x)^6-(1/8)*cos(2*x)^4. trigsin() of this result gives -(1/16)*sin(2*x)^8-(1/12)*sin(2*x)^6-(1/48). Calling ratnormal() on this gives us (-3*(sin(2*x))^8+4*(sin(2*x))^6-1)/48. If we wished, we could drop the 1/48 term, since it's an indefinite integral. So, dropping the constant and calling trigexpand on this, the result is -16*(cos(x)^8)*(sin(x)^8)-(16/3)*(cos(x)^6)*(sin(x)^6). Likewise, taking the original integral result and calling tcollect() on it, the result is -(3/256)*cos(4*x)-(1/512)*cos(8*x)-(1/768)*cos(12*x)-(1/2048)*cos(16*x)-(73/6144). Again, since it's an indefinite integral, the constant term at the end can be dropped.

In summary, have a trig expression and want to break it down to certain terms:

  • trigcos: Breaks it down in terms of cos.
  • trigsin: Breaks it down in terms of sin.
  • trigtan: Breaks it down in terms of tan.
  • tcollect: Converts from powers of trig functions to functions of n*x. Converts products to sums.
  • trigexpand: Converts to expression in terms of sin(x) and cos(x).
  • ratnormal: Changes different fractions in each term to one big irreducible fraction.
prime/misctips.1508488124.txt.gz · Last modified: 2017/10/20 01:28 by webmasterpdx