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aherbert pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/commons-numbers.git
commit f0b16526090ce2f0a81297e7c5728b758f988133
Author: Alex Herbert <aherb...@apache.org>
AuthorDate: Wed Oct 20 22:01:35 2021 +0100
Align multi-line mathjax equations
---
.../apache/commons/numbers/complex/Complex.java | 34 +++++++++++++---------
1 file changed, 20 insertions(+), 14 deletions(-)
diff --git
a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
index c795e28..2c9072b 100644
---
a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
+++
b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java
@@ -272,8 +272,9 @@ public final class Complex implements Serializable {
* Creates a complex number from its polar representation using modulus
{@code rho} (\( \rho \))
* and phase angle {@code theta} (\( \theta \)).
*
- * \[ x = \rho \cos(\theta) \\
- * y = \rho \sin(\theta) \]
+ * \[ \begin{aligned}
+ * x &= \rho \cos(\theta) \\
+ * y &= \rho \sin(\theta) \end{aligned} \]
*
* <p>Requires that {@code rho} is non-negative and non-NaN and {@code
theta} is finite;
* otherwise returns a complex with NaN real and imaginary parts. A {@code
rho} value of
@@ -647,8 +648,9 @@ public final class Complex implements Serializable {
* <a
href="http://mathworld.wolfram.com/ComplexConjugate.html";>conjugate</a>
* \( \overline{z} \) of this complex number \( z \).
*
- * <p>\[ z = a + i b \\
- * \overline{z} = a - i b \]
+ * <p>\[ \begin{aligned}
+ * z &= a + i b \\
+ * \overline{z} &= a - i b \end{aligned}\]
*
* @return The conjugate (\( \overline{z} \)) of this complex number.
*/
@@ -660,8 +662,9 @@ public final class Complex implements Serializable {
* Returns a {@code Complex} whose value is the negation of both the real
and imaginary parts
* of complex number \( z \).
*
- * <p>\[ z = a + i b \\
- * -z = -a - i b \]
+ * <p>\[ \begin{aligned}
+ * z &= a + i b \\
+ * -z &= -a - i b \end{aligned} \]
*
* @return \( -z \).
*/
@@ -1025,8 +1028,9 @@ public final class Complex implements Serializable {
* by \( i \) using a factor with magnitude 1.0. This should be used in
preference to
* {@link #multiply(Complex) multiply(Complex.I)} with or without {@link
#negate() negation}:</p>
*
- * \[ iz = (-b + i a) \\
- * -iz = (b - i a) \]
+ * \[ \begin{aligned}
+ * iz &= (-b + i a) \\
+ * -iz &= (b - i a) \end{aligned} \]
*
* <p>This method is included for compatibility with ISO C99 which defines
arithmetic between
* imaginary-only and complex numbers.</p>
@@ -1779,9 +1783,10 @@ public final class Complex implements Serializable {
*
* <p>This is implemented using real \( x \) and imaginary \( y \) parts:
*
- * <p>\[ \sin^{-1}(z) = \sin^{-1}(B) + i\ \text{sgn}(y)\ln \left(A +
\sqrt{A^2-1} \right) \\
- * A = \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} + \sqrt{(x-1)^2+y^2}
\right] \\
- * B = \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} - \sqrt{(x-1)^2+y^2}
\right] \]
+ * <p>\[ \begin{aligned}
+ * \sin^{-1}(z) &= \sin^{-1}(B) + i\ \text{sgn}(y)\ln \left(A +
\sqrt{A^2-1} \right) \\
+ * A &= \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} + \sqrt{(x-1)^2+y^2}
\right] \\
+ * B &= \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} - \sqrt{(x-1)^2+y^2}
\right] \end{aligned} \]
*
* <p>where \( \text{sgn}(y) \) is the sign function implemented using
* {@link Math#copySign(double,double) copySign(1.0, y)}.
@@ -1973,9 +1978,10 @@ public final class Complex implements Serializable {
*
* <p>This function is implemented using real \( x \) and imaginary \( y
\) parts:
*
- * <p>\[ \cos^{-1}(z) = \cos^{-1}(B) - i\ \text{sgn}(y) \ln\left(A +
\sqrt{A^2-1}\right) \\
- * A = \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} + \sqrt{(x-1)^2+y^2}
\right] \\
- * B = \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} - \sqrt{(x-1)^2+y^2}
\right] \]
+ * <p>\[ \begin{aligned}
+ * \cos^{-1}(z) &= \cos^{-1}(B) - i\ \text{sgn}(y) \ln\left(A +
\sqrt{A^2-1}\right) \\
+ * A &= \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} + \sqrt{(x-1)^2+y^2}
\right] \\
+ * B &= \frac{1}{2} \left[ \sqrt{(x+1)^2+y^2} - \sqrt{(x-1)^2+y^2}
\right] \end{aligned} \]
*
* <p>where \( \text{sgn}(y) \) is the sign function implemented using
* {@link Math#copySign(double,double) copySign(1.0, y)}.
