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Wolfram|Alpha Notebook Edition Turns One: Now with Support for Chemistry, Demonstrations and More

Brad Janes, Peter Falloon, Jeremy Stratton-Smith, Jason Sonnenberg

Author

Brad Janes, Peter Falloon, Jeremy Stratton-Smith, Jason Sonnenberg

Title

Wolfram|Alpha Notebook Edition Turns One: Now with Support for Chemistry, Demonstrations and More

Description

Updates include even easier ways to build on previous computations. Access Wolfram Function Repository functions. Solve chemistry problems with step-by-step help. Pull in thousands of interactive Demonstrations. Access in the cloud.

Wolfram|Alpha Notebook Edition Turns One: Now with Support for Chemistry, Demonstrations and More

September 11, 2020

Brad Janes, Wolfram|Alpha Math Content Manager

Peter Falloon, Data & Semantics Engineering

Jeremy Stratton-Smith, Math Developer, Wolfram|Alpha Math Content

The Wolfram|Alpha Chemistry Team

Wolfram|Alpha Notebook Edition was released nearly a year ago, and we're proud to share what the team has been working on since. In addition to the improvements made to Wolfram|Alpha itself, new input and output suggestions were added. There were parsing fixes, additions to the Wolfram|Alpha-to-Wolfram Language translation and some of the normal improvements one would expect. There are also some bigger features and interesting new capabilities that we will explore in a bit more detail here.

If you haven't checked out Wolfram|Alpha Notebook Edition in a while, we'd like to invite you to revisit. With education looking a little different for many people right now, this could be a great time to explore this exciting new way to interface with Wolfram technologies.

One of the most useful features of any notebook-based computational environment is the ability to reuse the result of a prior calculation as the input to a new one. Using this, computations can be built up using an intuitive “step-by-step” approach and the need for cutting/pasting or retyping is reduced. In Wolfram|Alpha Notebook Edition, previous outputs can be referenced in a variety of ways, ranging from familiar Wolfram Language constructs such as %n or Out[n] to natural language expressions such as “simplify the last result,” “plot the above” or “square it.” In certain cases, an explicit reference needn’t even appear: e.g. if you input “y = sin(x^3)” followed by “make a plot,” Wolfram|Alpha Notebook Edition will infer that you want to make a plot of the previous equation. This functionality, which has been under continuous development since the release of this product, has recently been extended to leverage the powerful semantic capabilities that power the Suggestions Bar. This allows for context-dependent tailoring of results containing references to previous outputs based on the semantic types of those results. As we build out this functionality, you can expect to see Wolfram|Alpha Notebook Edition becoming even smarter in helping you to build up your computations.

Next is an example of a chain of inputs covering topics through a first-semester calculus course.

Computeasimplelimit.Ifnovaluetoapproachisspecified,thedefaultis0.



lim x^2/(1 - cos(x))

step-by-step solution

related computations

full Wolfram|Alpha results

In[]:=

Limit[x^2/(1-Cos[x]),x->0]

Out[]=

Define a function, such as

f(x)



set f(x) equal x^2/(1-cos(x))

full Wolfram|Alpha results

In[]:=

f[x_]:=x^2/(1-Cos[x])

Users can refer to

f(x)

when further investigating its behavior.



limit of f(x) as x goes to Pi

step-by-step solution

related computations

full Wolfram|Alpha results

In[]:=

Limit[f[x],x->Pi]

Out[]=

Quickly plot the computed limit and

f(x)



plot this and f(x)

related computations

full Wolfram|Alpha results

In[]:=

Plot[{Pi^2/2,f[x]},{x,-6.,6.},Evaluated->True]

Out[]=

	2 π 2
	f(x)

Use the limit of the difference quotient to compute the derivative of

f(x)



limit (f(x+h) - f(x))/h as h->0

step-by-step solution

related computations

full Wolfram|Alpha results

In[]:=

Limit[(f[x+h]-f[x])/h,h->0]

Out[]=

csc

(xsin(x)+2cos(x)-2)

Verify.



is this equal to f'(x)

full Wolfram|Alpha results

In[]:=

TrueQ[Simplify[%==

′

[x]]]

Out[]=

True

Let us build up another chain of queries, starting with a challenge problem from the Math Olympiad competition. The problem states:

First, set up a definition that defines the sequence.



set a(n)=a(n-1)+a(n-2)+a(n-3)

full Wolfram|Alpha results

In[]:=

a[n_]:=a[n-1]+a[n-2]+a[n-3]

Next, initialize the given values.



set a(1)=1, a(2)=2, a(3)=3

full Wolfram|Alpha results

In[]:=

a[1]=1;a[2]=2;a[3]=3

Out[]=

To make sure that Wolfram|Alpha Notebook Edition is interpreting everything in the expected way, try evaluating the next element in the sequence.



a(4)

full Wolfram|Alpha results

In[]:=

a[4]

Out[]=

You can also test your function to see if it matches your intuition, here adding together the given initial values for

a(2)

and

a(3)

, plus your computed value for

a(4)



does a[5] = 2+3+6

full Wolfram|Alpha results

In[]:=

TrueQ[Simplify[a[5]==2+3+6]]

Out[]=

True

Finally, evaluate the sum to answer the initial question.



sum a(i) from i = 1 to 25

related computations

full Wolfram|Alpha results

In[]:=

Sum[a[i],{i,1,25}]

Out[]=

4700769

These are the same steps that a computer science student might take to solve such a problem, but no computer language or coding was required. Only simple natural language statements were used to set up, test and solve the desired problem.

One of the aspects of Wolfram|Alpha Notebook Edition that has been greatly expanded over the past year is the use of resource functions that are developed and submitted by staff members. Similar to what Bob expressed in his recent blog post, we are also fans of the Wolfram Function Repository and have been hard at work making useful tools more accessible. These functions, while submitted by internal staff, go through the exact same review process as that of externally submitted resource functions, and are all publicly accessible via the Function Repository. With the release of Wolfram|Alpha Notebook Edition, the challenge arose of concisely representing the many highly specific kinds of computations that are available through the many pods returned for an input in Wolfram|Alpha.

For example, a topic frequently covered in calculus classes is calculating the arc length of a curve, say

y==

given some bounds. This is easily done in the Wolfram Language by running the following:

In[]:=

ArcLength[x^2,{x,0,1}]

Out[]=

+ArcSinh[2])

This acts as a bit of a black box to students who may be asked to set up an integral and then evaluate it. Through the use of resource functions, Wolfram|Alpha Notebook Edition is able to do this exactly.



arc length of x^2 for 0<x<1

full Wolfram|Alpha results

In[]:=

[◼]	ArcLengthIntegral

[x^2,{x,0,1}]

Out[]=

∫

1+4

x



evaluate that

step-by-step solution

related computations

full Wolfram|Alpha results

In[]:=

Integrate[Sqrt[1+4*x^2],{x,0,1}]

Out[]=

+ArcSinh[2])

While this may seem like a number of extra steps, it fills a pedagogical role in granting students the ability to, in some way, peek under the hood of math that otherwise is so efficiently done with built-in functions.

The use of resource functions in Wolfram|Alpha Notebook Edition also eases the transition into learning Wolfram Language syntax that might be a stumbling block for students and educators new to Wolfram technologies. One example of this is the setup of an interactive plot to visualize the scaling and translation of a function as you vary parameters—something not possible on the web at this time.



plot b+Sin[a x] varying a and b from 0 to 2

full Wolfram|Alpha results

In[]:=

[◼]	ManipulatePlot

[b+Sin[a*x],{x,-5.4,5.4},{{a,1},0,2},{{b,1},0,2}]

Out[]=

Vertical range

Horizontal range

Seeing the Wolfram Language interpretation of this input introduces users to the syntax of this ManipulatePlot function so they might be able to build up something more complicated themselves, and also introduces them to Wolfram Language syntax proper. This highlights one of the key elements of the development of resource functions for use in Wolfram|Alpha Notebook Edition: creating highly functional code that does specific tasks that might not fit within the overall Wolfram Language. Such functions provide easy access points to high-level content that is particularly useful in the education world. Another key question in this development process is how to represent all of the information that is accessible from a single input to Wolfram|Alpha. Consider the information accessible from a simple input “sin(x)”. There are resource functions (and corresponding Wolfram|Alpha Notebook Edition inputs) like the following, which not only produce similar information, but can also present it in interactive ways to build intuition and understanding.



function overview Sin[x]

full Wolfram|Alpha results

In[]:=

[◼]	FunctionOverview

[Sin[x],x,Reals,Dataset]

Out[]=

Function	y.Sin[x]
Domain	
Range	-1≤y.≤1
Period	6.28319
Parity	Odd
Roots	x 2π  1 if  1 ∈ 
Roots	x π+2π  1 if  1 ∈ 
SeriesExpansionAt0	x- 3 x 6 + 5 x 120 - 7 x 5040 + 9 x 362880 + 11 O[x]
Derivative	Cos[x]
IndefiniteIntegral	-Cos[x]
Extrema	 … 2 
InflectionPoints	{ … 2 }
StationaryPoints	 … 2 



curve analysis sin[x]

full Wolfram|Alpha results

In[]:=

[◼]	CurveAnalysis

[Sin[x],x]

As seen here, through the use of high-level resource functions, Wolfram|Alpha Notebook Edition is able to serve content similar to Wolfram|Alpha, but reformatted and restructured for the desktop environment.

Our implementation of the Wolfram Function Repository functions goes beyond purely mathematical exploits. Here, we can generate an image.



image of a cat

alternate interpretations

full Wolfram|Alpha results

Assuming "cat" is a species specification. Use as

referring to cat breeds

instead

In[]:=

domestic cat

SPECIES SPECIFICATION



image



Out[]=

We can then perform some image processing analysis by interpreting the image in various ways.



dog vision of that

full Wolfram|Alpha results

In[]:=

[◼]	SimulateAnimalVision

["Dog",%]

Out[]=

Of course, the opposite is possible as well.



cat vision of a dog image

full Wolfram|Alpha results

In[]:=

[◼]	SimulateAnimalVision

"Cat",

dog	SPECIES SPECIFICATION



image



Out[]=

There are many other popular Wolfram|Alpha domains that are now directly supported in Wolfram|Alpha Notebook Edition.



orbit of halley's comet

alternate interpretations

full Wolfram|Alpha results

Assuming orbit is referring to orbital properties of a comet. Use "orbit" as

orbit circumference of a comet

. Use "the input" as

a formula

In[]:=

Wolfram|Alpha pod

Out[]=



Polaris sky chart from Seattle on 9/13/2020

alternate interpretations

full Wolfram|Alpha results

Assuming chart is referring to referring to a calendar computation. Use "sky chart" as

sky chart of a star

In[]:=

[◼]

SkyChart



Polaris

STAR

Seattle

CITY

["Position"],DateObject[{2020,9,13}]

Out[]=

	N
E		W
	S



play sin(x*Floor(100x^2)) for 5 seconds

full Wolfram|Alpha results

In[]:=

Play[Sin[x*Floor[100*x^2]],{x,0.3203475194016502,5.3203475194016505},SampleRate->44100]

Out[]=



plot eternatus curve

full Wolfram|Alpha results

In[]:=

Eternatus-like curve

POPULAR CURVE



plot



Out[]=



make the background pink

alternate interpretations

full Wolfram|Alpha results

Assuming basic pink. Use

HTML pink

instead

In[]:=

Show[%,Background->Pink]

Out[]=

One of the major new content areas that we’ve added support for in Wolfram|Alpha Notebook Edition is chemistry. How does the Wolfram|Alpha chemistry team prioritize which chemistry problems to support? We try to maximize the breadth of support while focusing on topics that are encountered in middle-school, high-school and college chemistry courses. Currently, we are working our way toward buffer problems by building up the prerequisite topics of solution preparation:



Prepare a 0.02 M KOH solution

full Wolfram|Alpha results

In[]:=

Wolfram|Alpha pod

Out[]=

dilute 0.00133L of concentrated(15M)potassium hydroxide to a final volume of 1L

... chemical equation balancing:



Balance Oxalic acid (s) + water (l) -> hydronium ion (aq) + oxalate ion (aq)

full Wolfram|Alpha results

In[]:=

Wolfram|Alpha pod

Out[]=

H (s)+2

O (l) ⟶ 2

(aq)+

(aq)

... and construction of the equilibrium constant expression:



equilibrium constant acetic acid (l) + water (l) -> hydronium ion (aq) + acetate ion (aq)

alternate interpretations

full Wolfram|Alpha results

Assuming acetate anion. Use

cyanide anion

instead

In[]:=

Wolfram|Alpha pod

Out[]=

 [

][

]

You can also see the step-by-step procedure of computing the previous chemistry results. We’ve also added support for the chemical capabilities newly added to the Wolfram Language in Version 12.



caffeine

alternate interpretations

full Wolfram|Alpha results

Assuming "caffeine" is a chemical compound. Use as

referring to molecule

a word

a movie

instead

In[]:=

caffeine

CHEMICAL

Out[]=

caffeine



molecule of that

full Wolfram|Alpha results

In[]:=

Molecule[%]

Out[]=

Molecule

Formula:

Atoms: 24 Bonds: 25



We are still building the kinds of chemical properties that work via session referencing, but many properties already work as a single-line input. These and more will be working via session referencing as well in the coming weeks.



(2R)-2-acetamido-3-methylbutanoic acid mesh region

full Wolfram|Alpha results

In[]:=

[◼]	MoleculeMeshRegion

[Molecule["(2R)-2-acetamido-3-methylbutanoic acid"]]

Out[]=



(2R)-2-acetamido-3-methylbutanoic acid principal moments of inertia

full Wolfram|Alpha results

In[]:=

MoleculeValue[Molecule["(2R)-2-acetamido-3-methylbutanoic acid"],"PrincipalMoments"]

Out[]=



324.135

677.81

798.115



Another tool in the Wolfram family that we have been able to add support for in Wolfram|Alpha Notebook Edition that is unavailable on the Wolfram|Alpha website is the Wolfram Demonstrations Project. In Wolfram|Alpha Notebook Edition, you can ask for a specific Demonstration by name. Clicking the entity blob will return the fully interactive Demonstration in a new window.



Mondrian Four-Coloring demonstration

full Wolfram|Alpha results

In[]:=

Mondrian Four-Coloring

WOLFRAM DEMONSTRATION

Out[]=

Mondrian Four-Coloring

You can also search Demonstrations by category if you are looking for a particular topic to, for instance, show off to your classroom. First, enter a query for Demonstrations of a particular category.



Derivatives demonstrations

alternate interpretations

full Wolfram|Alpha results

Assuming the input is referring to referring to wolfram demonstration data. Use as

referring to English words

instead. Use "Derivatives" as

referring to a mathematical definition

In[]:=

derivatives demonstrations

WOLFRAM DEMONSTRATIONS

Out[]=

derivatives demonstrations

The first item on the generated Suggestions Bar should be “entity list.” Click that to see the full EntityList of Demonstrations from that category.

In[]:=

EntityList

derivatives demonstrations

WOLFRAM DEMONSTRATIONS



Out[]=



A Fifth-Degree Polynomial and Its Derivatives

A Generalization of the Mean Value Theorem

An Ordinary Fractional Differential Equation

Approximating the Derivative by the Symmetric Difference Quotient

Approximating the Tangent to a Curve with Secants

A Semi-Discrete Analog to The Mean Value Theorem

A Snowball's Rate of Change

Automatic Differentiation

Calculus Slalom

Car Traveling at Night

Cauchy Mean-Value Theorem

Complex Newton Map

Complex Polynomials

Complex Roots of a Polynomial and Its Derivative

Cross-Sections of a Surface and Partial Derivatives

Cyclic Functions under Differentiation

Derivative as a Function

Derivative of a Vector-Valued Function in 2D

Derivative of log(x!)

Derivatives: A Look at Graphs

Derivatives of Exponential Functions

Derivatives of Quintic Polynomials

Derivatives of Sine

Derivatives of the Sum of Two Sines

Derivatives of Trig and Hyperbolic Functions

Differential of a Function

Directional Derivatives and the Gradient

Directional Derivatives in 3D

Family of Curves, Tangents, and Intuition

Fermat's Theorem on Stationary Points

Finding a Tangent Line to a Parabola

Finite Difference Approximations of the First Derivative of a Function

Finite Difference Schemes of One Variable

Flett's Theorem

Fractional Derivative of a Power

Fractional Derivative of Sine

Geometric Difference between a Finite Difference and a Differential

Gradients in 2D and 3D

Graphing Derivatives

Graphs of Taylor Polynomials

How the Area of a Disk Grows

Instantaneous Rate of Change

Instantaneous Rate of Change: Exploring More Functions with the First and Second Derivatives

Iterating Linear Functions

Jensen's Disks

Lagrange Multipliers in One Dimension

L'Hospital's Rule for 0/0 Forms

Marginal Utility Budget Line

Maximizing the Volume of a Right Circular Cone with Given Slant Length

Maximum Area Field with a Corner Wall

Mean Value Theorem

Multiple Derivatives

Non-Sinusoidal Oscillation: A Balloon on a String

Partial Derivative Functions and Their Plots

Partial Derivatives in 3D

Pathological Derivatives

Polynomial and Derivative

Polynomials and Derivatives

Related Rates Clock

Related Rates: Triangle Angle and Area

Route, Speed, and Acceleration of Your Mouse

Second-Order Partial Derivatives

Sendov's Conjecture

Slope between Two Points on a Curve

Snowboarding over Derivatives

Soil Temperature

Successive Derivatives of a Polynomial

Takagi Curve

Tangent Planes on a 3D Graph

Tangent Planes to Quadratic Surfaces

Tangent to a Curve

Tangent to a Surface

The Derivative of a to the Power x

The Envelope Theorem: Numerical Examples

The Fundamental Theorem of Calculus

The Geometry of Lagrange Multipliers

The Greatest Fenced Area along a Barn

The Product Rule

The Quotient Rule

The Schwarzian Derivative of Iterated Functions

The Tangent Line Problem

Total Differential of the First Order

Using Sampled Data to Estimate Derivatives, Integrals, and Interpolated Values

Velocity of a Falling Object



Beyond the Demonstrations, there are more ways to use Wolfram|Alpha Notebook Edition as a learning tool. Entering in a generic topic will, just as with the Wolfram|Alpha website, return a page with examples. This similarly pops up in a new notebook, pre-filled with sample natural language inputs in the domain that you were asking about.



differential equations

alternate interpretations

Assuming "differential equations" is a general topic. Use as

a computation

referring to a mathematical definition

a periodical

instead

Out[]=

NotebookObject

Untitled-4



This will encourage further exploration, as you will still see the same input and output suggestions as you would with your own inputs. And speaking of example pages, a new project we’re working on that will be particularly useful for educators in the US is curated examples pages catered to the US Common Core Math Standards. An example of what that will look like follows, and we are planning on releasing pages for all the US standards in the coming months.

Perhaps our latest and most exciting addition to the world of Wolfram|Alpha Notebook Edition is the migration of our Wolfram|Alpha notebook capabilities to the Wolfram Cloud. Now you can do all kinds of computational exploration from your browser. To access this feature, navigate to File > New > Wolfram|Alpha-Mode Notebook. You should see the familiar natural language input box, and you can now enter the same kinds of queries, view input and output suggestions and even interact with our Demonstrations and built-in Function Repository functions!

We are proud of the progress we have made in the last year, and we are especially encouraged by the number of people trying Wolfram|Alpha Notebook Edition and the kinds of computations that they are using it for. We hope it will continue to be a useful tool for students, educators, parents, independent researchers and enthusiasts. Please let us know what else you’d like to see in Wolfram|Alpha Notebook Edition!

Also keep an eye out for upcoming book releases from Wolfram Media:

Click here to receive updates about the third edition of Hands-on Start to Wolfram Mathematica and Programming with the Wolfram Language.

Click here to receive updates about Hands-on Start to Wolfram|Alpha Notebook Edition.

Cite this as: Brad Janes, Peter Falloon, Jeremy Stratton-Smith, Jason Sonnenberg, "Wolfram|Alpha Notebook Edition Turns One: Now with Support for Chemistry, Demonstrations and More" from the Notebook Archive (2020), https://notebookarchive.org/2020-09-54kgk8e