I need help

[Proektsoftbg]

Can someone translate this new readme text for version 7.5.8 to Chinese please:

        <p>It finds the value of the first derivative of a real function <b>f</b>(<var>x</var>) at the specified point <var>x</var> = <var>a</var>. The derivative represents the slope of the tangent to the function at point <var>a</var>. There are two methods that you can use in Calcpad:
        <p style="margin-left: 2em;"><code><span class="cond">$Slope</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code> - uses symmetric two-point finite difference with <a href="https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1911.0009">Richardson extrapolation</a>. It evaluates the derivative within the specified <var>Precision</var>. The function must be locally continuous, smooth and differentiable in the neighborhood of <var>a</var>. It can also contain other numerical methods. In general, finite differences are susceptible to floating point round-off errors due to the subtraction of close values. Although Richardson extrapolation can improve this significantly, the accuracy for poorly behaved functions may be limited.</p>
        <p style="margin-left: 2em;"><code><span class="cond">$Derivative</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code> - uses complex step method (<a href="https://epubs.siam.org/doi/abs/10.1137/0704019">Lyness and Moler</a>). It evaluates the derivative with nearly machine precision (10<sup>&hairsp;-15</sup> to 10<sup>&hairsp;-16&hairsp;</sup>) by using the equation: <var>f</var>&thinsp;′(<var>a</var>) = <b>Im</b>(&thinsp;<var>f</var>&thinsp;(<var>a</var>+<var>ih</var>))/<var>h</var>, where <var>i</var> is the imaginary unit and <var>h</var> = 10<sup>-20</sup>. The function must be holomorphic in the complex plane - infinitely differentiable and locally equal to its Taylor expansion. Unlike <code class="cond">$Slope</code>, it cannot contain other numerical methods and should be defined only by analytic expressions. This limits the applicability of this method but, if possible, you can use it instead of <code class="cond">$Slope</code> to achieve higher accuracy when required.</p>

I do not trust automatic translations especially when I understand nothing of the language. @idealkindom ?

[idealkindom]

I Will Finsh it today later. 在 2025-12-29 22:50:45，"Ned Ganchovski" ***@***.***> 写道： Can someone translate this new readme text for version 7.5.8 to Chinese please: <p>It finds the value of the first derivative of a real function <b>f</b>(<var>x</var>) at the specified point <var>x</var> = <var>a</var>. The derivative represents the slope of the tangent to the function at point <var>a</var>. There are two methods that you can use in Calcpad: <p style="margin-left: 2em;"><code><span class="cond">$Slope</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code> - uses symmetric two-point finite difference with <a href="https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1911.0009">Richardson extrapolation</a>. It evaluates the derivative within the specified <var>Precision</var>. The function must be locally continuous, smooth and differentiable in the neighborhood of <var>a</var>. It can also contain other numerical methods. In general, finite differences are susceptible to floating point round-off errors due to the subtraction of close values. Although Richardson extrapolation can improve this significantly, the accuracy for poorly behaved functions may be limited.</p> <p style="margin-left: 2em;"><code><span class="cond">$Derivative</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code> - uses complex step method (<a href="https://epubs.siam.org/doi/abs/10.1137/0704019">Lyness and Moler</a>). It evaluates the derivative with nearly machine precision (10^&hairsp;-15 to 10^{&hairsp;-16&hairsp;}) by using the equation: <var>f</var>&thinsp;′(<var>a</var>) = <b>Im</b>(&thinsp;<var>f</var>&thinsp;(<var>a</var>+<var>ih</var>))/<var>h</var>, where <var>i</var> is the imaginary unit and <var>h</var> = 10^-20. The function must be holomorphic in the complex plane - infinitely differentiable and locally equal to its Taylor expansion. Unlike <code class="cond">$Slope</code>, it cannot contain other numerical methods and should be defined only by analytic expressions. This limits the applicability of this method but, if possible, you can use it instead of <code class="cond">$Slope</code> to achieve higher accuracy when required.</p> I do not trust automatic translations especially when I understand nothing of the language. @idealkindom ? — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you were mentioned.Message ID: ***@***.***>

[idealkindom]

Can someone translate this new readme text for version 7.5.8 to Chinese please:

        <p>It finds the value of the first derivative of a real function <b>f</b>(<var>x</var>) at the specified point <var>x</var> = <var>a</var>. The derivative represents the slope of the tangent to the function at point <var>a</var>. There are two methods that you can use in Calcpad:
        <p style="margin-left: 2em;"><code><span class="cond">$Slope</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code> - uses symmetric two-point finite difference with <a href="https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1911.0009">Richardson extrapolation</a>. It evaluates the derivative within the specified <var>Precision</var>. The function must be locally continuous, smooth and differentiable in the neighborhood of <var>a</var>. It can also contain other numerical methods. In general, finite differences are susceptible to floating point round-off errors due to the subtraction of close values. Although Richardson extrapolation can improve this significantly, the accuracy for poorly behaved functions may be limited.</p>
        <p style="margin-left: 2em;"><code><span class="cond">$Derivative</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code> - uses complex step method (<a href="https://epubs.siam.org/doi/abs/10.1137/0704019">Lyness and Moler</a>). It evaluates the derivative with nearly machine precision (10<sup>&hairsp;-15</sup> to 10<sup>&hairsp;-16&hairsp;</sup>) by using the equation: <var>f</var>&thinsp;′(<var>a</var>) = <b>Im</b>(&thinsp;<var>f</var>&thinsp;(<var>a</var>+<var>ih</var>))/<var>h</var>, where <var>i</var> is the imaginary unit and <var>h</var> = 10<sup>-20</sup>. The function must be holomorphic in the complex plane - infinitely differentiable and locally equal to its Taylor expansion. Unlike <code class="cond">$Slope</code>, it cannot contain other numerical methods and should be defined only by analytic expressions. This limits the applicability of this method but, if possible, you can use it instead of <code class="cond">$Slope</code> to achieve higher accuracy when required.</p>

I do not trust automatic translations especially when I understand nothing of the language. @idealkindom ?

The Chinese translations come:

        <p>该函数求实函数<b>f</b>(<var>x</var>)在指定点<var>x</var> = <var>a</var>的一阶导数. 导数即函数在点 <var>a</var>的切线斜率. 在Calcpad中用户可以采用两种方法:
        <p style="margin-left: 2em;"><code><span class="cond">$Slope</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code>:采用带<a href="https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1911.0009"> Richardson外插</a>的对称2点有限差分.该方法在指定精度<var>Precision</var>范围内计算导数.函数必须局部连续、平滑且在<var>a</var>的邻域内可导. 该方法也可以包含其他数值方法.一般有限差分法容易导致由于接近值之间的减法造成的浮点舍入误差. 即便Richardson外插可以显著地改善该问题,但对不规则函数的精度依然有限.</p>
        <p style="margin-left: 2em;"><code><span class="cond">$Derivative</span>{<b>f</b>(<var>x</var>) &#64; <var>x</var> = <var>a</var>}</code>:采用复数(<a href="https://epubs.siam.org/doi/abs/10.1137/0704019">Lyness and Moler</a>)分步法. 其通过使用以下方程:<var>f</var>&thinsp;′(<var>a</var>) = <b>Im</b>(&thinsp;<var>f</var>&thinsp;(<var>a</var>+<var>ih</var>))/<var>h</var>从而以接近机器精度(10<sup>&hairsp;-15</sup> ~10<sup>&hairsp;-16&hairsp;</sup>)计算导数, 其中<var>i</var>为虚部单位,<var>h</var> = 10<sup>-20</sup>.函数在复平面中必须全纯(holomorphic),即无穷可导且局部等于其泰勒展开. 与 <code class="cond">$Slope</code>不同, 该方法不能包含其他数值方法且只能通过解析表达式定义. 这限制了该方法的可应用性,但是当有要求时，如果可能用户应尽可能用该函数而非<code class="cond">$Slope</code> 以获得更高精度.</p>

[Proektsoftbg]

@idealkindom thank you so much for your kind help and your quick responce. Chinese text looks so beautiful, but unfortunately I do not understand anything. Now I can update also the Chinese version to 7.5.8 with the latest improvements.

[idealkindom]

Of course Ned.

…

-- 发自我的网易邮箱手机智能版 在 2026-01-01 00:12:40，"Ned Ganchovski" ***@***.***> 写道： @idealkindom thank you so much for your kind help and your quick responce. Chinese text looks so beautiful, but unfortunately I do not understand anything. Now I can update also the Chinese version to 7.5.8 with the latest improvements. — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you were mentioned.Message ID: ***@***.***>