## 用MATHEMATICA计算一元高次方程（续）

StartYear是起始年份，EndYear是结束年份，Year是一共经历了多少年。

StartNumber 就是初始年份的值，EndNumber是结束年份的值。

## 用Mathematica的 DSolve 解微分方程时返回True的原因和解决办法

Question: DSolve returns true

Using Mathematica 7, I got a solution

The only time I was able to reproduce the “DSolve[True….” message was when I had the sequence of commands as follows,

What’s happening is that y'[x] is known to be x- y[x], and the DSolve is doing a compare of y-y[x] == y-y[x], returning True. Then it can’t solve True for y[x] in x, resulting in the question being returned.

Would you try exiting the kernel, restart fresh, and re-typing (* commands 1*) only.

（内容出自 Wolfram Community http://community.wolfram.com/groups/-/m/t/332674

# 控件对象

Wolfram 语言提供一系列完整的控件对象，所有对象以便捷的符号形式表示. Manipulate 自动调用这些对象；您也可以在一般输入时直接调用它们，或在您自己的动态界面内调用它们.

Control 一个自动选择类型的交互控制

IntervalSlider 使用下界和上界设值

ColorSlider 交互选择一个颜色

Setter 设置按下鼠标时的值:

Toggler 点击时切换值

ListPicker 选项列表

InputField 可接受字符串、数字或任何表达式的输入栏

FormControl 含有释义明确的字段的任意表单

LocatorPane 图形或其它背景上可移动的定位器

Button 可以设置任意外观和行为的按钮

PasteButton 复制表达式的按钮

EventHandler 低层次事件处理

FileNameSetter 系统文件浏览

ColorSetter 系统颜色选择

FormObject 指定格式结构

FormFunction 设置活动的可提交格式

# 相关教程

## 计算张量的软件

EDC and RGTC，即 Riemannian Geometry & Tensor Calculus @ Mathematica，链接：http://www.inp.demokritos.gr/~sbonano/RGTC/

• Download all files – compressed: .sit format (100 KB), .zip format (135 KB)
• Uncompressed files (~1000 KB):  RGTC.nb  —  OperatorPLT.nb  —  NPsymbolPLT.nb  —  EDCRGTCcode.m. (Only the combined matrixEDC and RGTC code in package format is included — it must be placed in an appropriate directory).
• Note: RGTC cannot be used for calculations with abstract tensors (manipulation of tensor expressions with abstract indices). It only operates on explicit tensors (nested lists of components which are functions of the coordinates). For abstract calculations try the package xTensor.

Additional Examples can be found here.

## Standalone software

• SPLATT[1] is an open source software package for high-performance sparse tensor factorization. SPLATT ships a stand-alone executable, C/C++ library, and Octave/MATLABAPI.
• Cadabra[2] is a computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many more. The input format is a subset of TeX. Both a command-line and a graphical interface are available.
• Tela[3] is a software package similar to Matlab and (GNU) Octave, but designed specifically for tensors.

## Software for use with Mathematica

• Tensor[4] is a tensor package written for the Mathematica system. It provides many functions relevant for General Relativity calculations in general Riemann-Cartan geometries.
• Ricci[5] is a system for Mathematica 2.x and later for doing basic tensor analysis, available for free.
• TTC[6] Tools of Tensor Calculus is a Mathematica package for doing tensor and exterior calculus on differentiable manifolds.
• EDC and RGTC,[7] “Exterior Differential Calculus” and “Riemannian Geometry & Tensor Calculus,” are free Mathematica packages for tensor calculus especially designed but not only for general relativity.
• Tensorial[8] “Tensorial 4.0” is a general purpose tensor calculus package for Mathematica.
• xAct:[9] Efficient Tensor Computer Algebra for Mathematica. xAct is a collection of packages for fast manipulation of tensor expressions.
• GREAT[10] is a free package for Mathematica that computes the Christoffel connection and the basic tensors of General Relativity from a given metric tensor.
• Atlas 2 for Mathematica[11] is a powerful Mathematica toolbox which allows to do a wide range of modern differential geometry calculations
• GRTensorM[12] is a computer algebra package for performing calculations in the general area of differential geometry.
• MathGR[13] is a package to manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices to partially or completely explicit indices and convert partial derivatives into total derivatives.
• TensoriaCalc[14] is a tensor calculus package written for Mathematica 9 and higher, aimed at providing user-friendly functionality and a smooth consistency with the Mathematica language itself. As of January 2015, given a metric and the coordinates used, TensoriaCalc can compute Christoffel symbols, the Riemann curvature tensor, and Ricci tensor/scalar; it allows for user-defined tensors and is able to perform basic operations such as taking the covariant derivatives of tensors. TensoriaCalc is continuously under development due to time constraints faced by its inventor/developer.

## Software for use with Maple

• GRTensorII[15] is a computer algebra package for performing calculations in the general area of differential geometry.
• Atlas 2 for Maple[16] is a modern differential geometry for Maple.
• DifferentialGeometry[17] is a package which performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, General Relativity, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. It is included with Maple.

## Software for use with Maxima

Maxima[23] is a free open source general purpose computer algebra system which includes several packages for tensor algebra calculations in its core distribution. It is particularly useful for calculations with abstract tensors, i.e., when one wishes to do calculations without defining all components of the tensor explicitly. It comes with three tensor packages:[24]

• itensor for abstract (indicial) tensor manipulation,
• ctensor for component-defined tensors, and
• atensor for algebraic tensor manipulation.

## Software for use with R

• Tensor[25] is an R package for basic tensor operations.
• rTensor[26] provides several tensor decomposition approaches.
• tensorBF[27] is an R package for Bayesian Tensor decomposition.
• MTF[28] Bayesian Multi-Tensor Factorization for data fusion and Bayesian versions of Tensor PCA and Tensor CCA. Software: MTF

## Libraries

• Redberry[29] is an open source computer algebra system designed for symbolic tensor manipulation. Redberry provides common tools for expression manipulation, generalized on tensorial objects, as well as tensor-specific features: indices symmetries, LaTeX-style input, natural dummy indices handling, multiple index types etc. The HEP package includes tools for Feynman diagrams calculation: Dirac and SU(N) algebra, Levi-Civita simplifications, tools for calculation of one-loop counterterms etc. Redberry is written in Java and provides extensive Groovy-based programming language.
• libxm[30] is a lightweight distributed-parallel tensor library written in C.
• FTensor[31] is a high performance tensor library written in C++.
• TL[32] is a multi-threaded tensor library implemented in C++ used in Dynare++. The library allows for folded/unfolded, dense/sparse tensor representations, general ranks (symmetries). The library implements Faa Di Bruno formula and is adaptive to available memory. Dynare++ is a standalone package solving higher order Taylor approximations to equilibria of non-linear stochastic models with rational expectations.
• vmmlib[33] is a C++ linear algebra library that supports 3-way tensors, emphasizing computation and manipulation of several tensor decompositions.
• Spartns[34] is a Sparse Tensor framework for Common Lisp.
• FAstMat[35] is a thread-safe general tensor algebra library written in C++ and specially designed for FEM/FVM/BEM/FDM element/edge wise computations.
• Cyclops Tensor Framework [36] is a distributed memory library for efficient decomposition of tensors of arbitrary type and parallel MPI+OpenMP execution of tensor contractions/functions.
• TiledArray[37] is a scalable, block-sparse tensor library that is designed to aid in rapid composition of high-performance algebraic tensor equation. It is designed to scale from a single multicore computer to a massively-parallel, distributed-memory system.
• libtensor [38] is a set of performance linear tensor algebra routines for large tensors found in post-Hartree-Fock methods in quantum chemistry.
• ITensor [39] features automatic contraction of matching tensor indices. It is written in C++ and has higher-level features for quantum physics algorithms based on tensor networks.
• Fastor [40] is a high performance C++ tensor algebra library that supports tensors of any arbitrary dimensions and all their possible contraction and permutation thereof. It employs compile-time graph search optimisations to find the optimal contraction sequence between arbitrary number of tensors in a network. It has high level domain specific features for solving nonlinear multiphysics problem using FEM.
• Xerus [41] is a C++ tensor algebra library for tensors of arbitrary dimensions and tensor decomposition into general tensor networks (focusing on matrix product states). It offers Einstein notation like syntax and optimizes the contraction order of any network of tensors at runtime so that dimensions need not be fixed at compile-time.

## 用Mathematica计算一元高次方程

$15000 (1+x)^{10}=20000$

15000*(1+x)^10=20000

1 清除单个变量

2 清除所有变量

## 在Mathematica中为某一个数值绘制指示说明

1. 使用虚线点为某一个数字进行说明，还可以做成可交互的文件。

var demoObj = new DEMOEMBED(); demoObj.run(‘SupplyAndDemand’, ”, ‘535’, ‘545’);

2. 使用箭头来标注

var demoObj = new DEMOEMBED(); demoObj.run(‘BernsteinPolynomials’, ”, ‘517’, ‘585’);

3 其他方法包括使用 Epilog 结合绘制 Arrow 来手动控制，比如

## 感悟：知乎上这几个答案震惊到我了

#### 第三个回答：

================================================

micro.ustc.edu.cnML/DataMining我只看过一些些，这些东西如果自己写算法的话需要用c/cpp如果只是玩玩可以用python+一堆库的方式来搞。主要可能还是数据源吧。嵌入式&单片机，如果不慎入实验物理坑会点单片机嵌入式还是有必要的，入个树莓派玩玩ROS吧。从树莓派+arduino玩的方式入手玩起来很简单无压力，最练手的就是写机器人控制了。这个是从机械折腾到前段的。

arduino是一种高度简化后的单片机。比起51等用起来真的简单多了

1.熟练使用linux/unix（格式化硬盘一个月内可以生存）
2.选一个自己顺手的IDE（vim/emacs/VS），基本熟练cpp、python（均指一万行代码，可以写写计算物理习题）
3.搭建一个自己的服务器（using aws.amazon.com ec2）
4.写一个桌面app .net/cocoa，（学c#/o-c），在这里折腾OpenGL CUDA等
5.写一个绚烂的个人网站use Django&html5&css3&webgl
6.研究妹子回你短信速度和她对你好感度的关系（使用支持向量机/deep learning）
7.学习CUDA并在你的pc上模拟EAST using MHD model in FEA
（其实能跑出来一个N-S方程出来个卡门涡街就很好了）
8.学习单片机并且控制一架四轴飞行器给那个追了四年没追的女神泼一盆冷水（someone你丫两年以后给我等着）。

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## 计算物理：对 Mathematica 中的黑洞热力学熵交互程序(CDF文件)的解释

Gerard ‘t Hooft and Leonard Susskind (2001) proposed a general “holographic principle” of nature, which suggests that consistent theories of gravity and quantum mechanics can be represented by lower-dimensional structures. Both the information paradox and the holographic principle remain active areas of investigation.