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Calculus example
Include the symja-YYYY-MM-DD.jar and the log4j-1.2.11.jar libraries in your classpath and start coding using parsed input strings or the internal object hierarchy.
Here are some calculus examples:
Example:
import static org.matheclipse.core.expression.F.*;
import org.matheclipse.core.basic.Config;
import org.matheclipse.core.eval.ExprEvaluator;
import org.matheclipse.core.interfaces.IAST;
import org.matheclipse.core.interfaces.IExpr;
import org.matheclipse.parser.client.SyntaxError;
import org.matheclipse.parser.client.math.MathException;
public class CalculusExample {
public static void main(String[] args) {
try {
// don't distinguish between lower- and uppercase identifiers
Config.PARSER_USE_LOWERCASE_SYMBOLS = true;
ExprEvaluator util = new ExprEvaluator(false, 100);
// Show an expression in the Java form:
// Note: single character identifiers are case sensistive
// (the "D()" function input must be written as upper case character)
String javaForm = util.toJavaForm("D(sin(x)*cos(x),x)");
// prints: D(Times(Sin(x),Cos(x)),x)
System.out.println(javaForm.toString());
// Use the Java form to create an expression with F.* static methods:
IAST function = D(Times(Sin(x), Cos(x)), x);
IExpr result = util.evaluate(function);
// print: Cos(x)^2-Sin(x)^2
System.out.println(result.toString());
// evaluate the string directly
// Note "diff" is an alias for the "D" function
result = util.evaluate("diff(sin(x)*cos(x),x)");
// print: Cos(x)^2-Sin(x)^2
System.out.println(result.toString());
// evaluate the last result ($ans contains "last answer")
result = util.evaluate("$ans+cos(x)^2");
// print: 2*Cos(x)^2-Sin(x)^2
System.out.println(result.toString());
// evaluate an Integrate[] expression
result = util.evaluate("integrate(sin(x)^5,x)");
// print: 2/3*Cos(x)^3-1/5*Cos(x)^5-Cos(x)
System.out.println(result.toString());
// set the value of a variable "a" to 10
// Note: in server mode the variable name must have a preceding '$' character
result = util.evaluate("a=10");
// print: 10
System.out.println(result.toString());
// do a calculation with variable "a"
result = util.evaluate("a*3+b");
// print: 30+b
System.out.println(result.toString());
// Do a calculation in "numeric mode" with the N() function
// Note: single character identifiers are case sensistive
// (the "N()" function input must be written as upper case character)
result = util.evaluate("N(sinh(5))");
// print: 74.20321057778875
System.out.println(result.toString());
// define a function with a recursive factorial function definition.
// Note: fac(0) is the stop condition which must be defined first.
result = util.evaluate("fac(0)=1;fac(x_IntegerQ):=x*fac(x-1)");
// now calculate factorial of 10:
result = util.evaluate("fac(10)");
// print: 3628800
System.out.println(result.toString());
} catch (SyntaxError e) {
// catch Symja parser errors here
System.out.println(e.getMessage());
} catch (MathException me) {
// catch Symja math errors here
System.out.println(me.getMessage());
} catch (Exception e) {
e.printStackTrace();
}
}
}
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