// calc tangent at x=a
@Override
public final void compute() {
double a = n.getDouble();
if (!f.isDefined() || !deriv.isDefined() || Double.isInfinite(a) || Double.isNaN(a)) {
tangent.setUndefined();
return;
}
// calc the tangent;
double fa = f.evaluate(a);
double slope = deriv.evaluate(a);
tangent.setCoords(-slope, 1.0, a * slope - fa);
T.setCoords(a, fa, 1.0);
}
public AlgoCompleteSquare(Construction cons, String label, GeoFunction f) {
super(cons);
this.f = f;
a = new MyDouble(kernel);
h = new MyDouble(kernel);
k = new MyDouble(kernel);
fv = new FunctionVariable(kernel);
ExpressionNode squareE = new ExpressionNode(kernel, a);
Function squareF = new Function(squareE, fv);
squareF.initFunction();
square = new GeoFunction(cons);
setInputOutput();
square.setFunction(squareF);
compute();
lastDeg = 0;
square.setLabel(label);
}
@Override
protected void applyCasCommand(StringTemplate tpl) {
StringBuilder sb = new StringBuilder();
sb.append("TrigCombine[%");
if (target != null) {
sb.append(',');
sb.append(target.toValueString(tpl));
}
sb.append(']');
g.setUsingCasCommand(sb.toString(), f, true, arbconst);
}
/**
* @param cons construction
* @param label label for output
* @param degree maximal degree
* @param min minimal coefficient vlaue
* @param max maximal coefficient value
*/
public AlgoRandomPolynomial(
Construction cons, String label, NumberValue degree, NumberValue min, NumberValue max) {
super(cons);
this.degree = degree;
this.min = min;
this.max = max;
fv = new FunctionVariable(kernel);
f = new Function(new ExpressionNode(kernel, fv), fv);
polynomial = new GeoFunction(cons);
setInputOutput();
compute();
polynomial.setLabel(label);
}
@Override
public void compute() {
// cover undefined cases
if (!degree.isDefined() || !min.isDefined() || !max.isDefined() || degree.getDouble() < 0) {
polynomial.setUndefined();
return;
}
int lower = (int) Math.ceil(min.getDouble());
int upper = (int) Math.floor(max.getDouble());
if (lower > upper || (lower == 0 && upper == 0)) {
polynomial.setUndefined();
return;
}
// input is sane, we can do the computation
int deg = (int) Math.floor(degree.getDouble());
ExpressionNode varExpr = new ExpressionNode(kernel, fv);
ExpressionNode newExpr = randomCoef(deg != 0);
for (int i = 1; i <= deg; i++) {
newExpr = varExpr.power(new MyDouble(kernel, i)).multiply(randomCoef(i != deg)).plus(newExpr);
}
f.setExpression(newExpr, fv);
polynomial.setFunction(f);
}
@Override
public void compute() {
int degInt;
GeoList coefs = null;
fv.setVarString(f.getVarString(StringTemplate.defaultTemplate));
// px^2+qx+r; p+q+r=s;
double r = f.evaluate(0);
double s = f.evaluate(1);
double p = 0.5 * (s + f.evaluate(-1)) - r;
double q = s - p - r;
boolean isQuadratic = !f.isGeoFunctionConditional();
double[] checkpoints = {1000, -1000, Math.PI, Math.E};
for (int i = 0; i < checkpoints.length; i++) {
double x = checkpoints[i];
if (!Kernel.isZero(p * x * x + q * x + r - f.evaluate(x))) {
// App.debug(p + "," + q + "," + r + ","
// + (p * x * x + q * x + r - f.evaluate(x)));
isQuadratic = false;
}
}
if (!isQuadratic) {
if (algoCoef == null) {
algoCoef = new AlgoCoefficients(cons, f);
algoCoef.setProtectedInput(true);
algoCoef.remove();
} else {
algoCoef.compute();
}
coefs = algoCoef.getResult();
degInt = coefs.size() - 1;
isQuadratic = coefs.isDefined() && coefs.get(0).isDefined();
for (int i = 1; i < degInt; i++) {
if (2 * i != degInt && !Kernel.isZero(((GeoNumeric) coefs.get(i)).getDouble())) {
isQuadratic = false;
}
p = ((GeoNumeric) coefs.get(0)).getDouble();
q = ((GeoNumeric) coefs.get(degInt / 2)).getDouble();
r = ((GeoNumeric) coefs.get(degInt)).getDouble();
}
} else {
degInt = 2;
}
if (degInt % 2 == 1 || degInt < 2 || !isQuadratic || Kernel.isZero(p)) {
square.setUndefined();
return;
}
if (lastDeg != degInt) {
ExpressionNode squareE;
ExpressionValue fvPower;
if (degInt == 2) fvPower = fv;
else
fvPower = new ExpressionNode(kernel, fv, Operation.POWER, new MyDouble(kernel, degInt / 2));
squareE =
new ExpressionNode(
kernel,
new ExpressionNode(
kernel,
a,
Operation.MULTIPLY,
new ExpressionNode(kernel, fvPower, Operation.MINUS, h)
.power(new MyDouble(kernel, 2))),
Operation.PLUS,
k);
square.getFunction().setExpression(squareE);
}
lastDeg = degInt;
fv.setVarString(f.getVarString(StringTemplate.defaultTemplate));
// if one is undefined, others are as well
square.setDefined(!Double.isNaN(r));
a.set(p);
h.set(-q / (2 * p));
k.set(r - q * q / (p * 4));
}
@Override
public final String toString(StringTemplate tpl) {
// Michael Borcherds 2008-03-30
// simplified to allow better Chinese translation
return getLoc().getPlain("TangentToAatB", f.getLabel(tpl), "x = " + ngeo.getLabel(tpl));
}