The Explain command asks a large language model to explain something. The item to be explained can be a string, an algebraic expression, a relation such as an equation or inequality, or a list or set of expressions or relations.

After an explanation, you can ask for more detail by issuing the command $\mathrm{Explain}\left(\mathrm{more}\right)$. This keyword can be given as a string or a name, and you can equivalently use the arguments $\mathrm{further}$, $\mathrm{continue}$, $\mathrm{go\; on}$, or $\mathrm{elaborate}$. Note that $\mathrm{go\; on}$ needs to be quoted because it contains a space.

Maple can interface with OpenAI's GPT-4 and ChatGPT models. The default model is GPT-4; you can select ChatGPT by using the $\mathrm{model}=\mathrm{ChatGPT}$ option, or force use of the GPT-4 model by using the $\mathrm{model}=\mathrm{GPT4}$ option. Note that OpenAI may deprecate and disable models, so the set of models supported may change in the future.

Note: Large language models often generate inaccurate statements. Please keep this in mind: this is not technology for building a bridge with.

$\mathrm{with}\left(\mathrm{NaturalLanguage}\right)\:$

$\mathrm{Explain}\left(x^2+y^2=1\right)$

$''This\; is\; the\; equation\; of\; a\; circle\; with\; radius\; 1\; centered\; at\; the\; origin\; (0,0)\; in\; the\; Cartesian\; coordinate\; system.''$

$\mathrm{Explain}\left(\mathrm{more}\right)$

$The equation x^2 + y^2 = 1 corresponds to a circle in the Euclidean plane. In detail, this is due to the Pythagorean theorem: in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this equation, you can think of the 'x' and 'y' as specifying any point in the plane, and the '1' on the right-hand side as specifying that the point is at a distance of 1 from the origin (0,0). So, this equation defines a circle centered at the origin with radius 1. The reason it's centered at the origin is because there are no 'x' or 'y' terms subtracted or added on the left-hand side (e.g., (x - h)^2 + (y - k)^2 = r^2 forms a circle with center at (h, k) and radius r). Also, because there's no coefficient multiplying the x^2 or y^2 term, it's not an ellipse but a circle, since the circle is the special case of an ellipse where the two axes are of equal length. It's one of the simplest examples of a conic section (the set of points in the plane satisfying a quadratic equation), and forms the basis for the complex numbers when geometrically interpreted.$

$\mathrm{Explain}\left(\mathrm{\Re }\left(\exp \left(x\mathrm{I}+y\mathrm{I}\right)\right)=\mathrm{\Re }\left(\exp \left(x\mathrm{I}\right)\right)\mathrm{\Re }\left(\exp \left(y\mathrm{I}\right)\right)-\mathrm{\Im }\left(\exp \left(x\mathrm{I}\right)\right)\mathrm{\Im }\left(\exp \left(y\mathrm{I}\right)\right)\right)$

$This equation is about the product of two complex numbers in polar form. In complex analysis, it's common to represent a complex number in polar form as e^(ix), where x is the angle measurement from the positive real axis. The equation is expressing the relation between the real part of the product of two complex numbers and the product of their real parts and imaginary parts separately. Re(e^(ix)) represents the real part of a complex number, and Im(e^(ix)) represents the imaginary part. The equation is essentially breaking down the multiplication of two complex numbers into their real and imaginary components. However, the given equation is not correct. According to the multiplication properties of complex numbers, if z1 = r1e^(iθ1) and z2 = r2e^(iθ2) are two complex numbers in polar form, the real part of the product z1z2 is obtained from the equation: Re(z1z2) = r1r2 cos(θ1 + θ2) = r1* r2*cos(θ1)*cos(θ2) - r1*r2*sin(θ1)*sin(θ2) which is Re(z1)*Re(z2) - Im(z1)*Im(z2) in rectangular coordinates. Thus, the correct relation for real parts should be: Re(e^(i(x+y))) = Re(e^(ix)) * Re(e^(iy)) - Im(e^(ix)) * Im(e^(iy)) .$

$\mathrm{Explain}\left(''go\; on''\,\mathrm{model}=\mathrm{ChatGPT}\right)$

$The equation Re(e^(i*x+i*y)) = Re(e^(i*x))*Re(e^(i*y))-Im(e^(i*x))*Im(e^(i*y)) is about expressing the real part of the complex number e^(i*x+i*y) in terms of the real and imaginary parts of e^(i*x) and e^(i*y). The complex number e^(i*x) represents a point on the unit circle in the complex plane, rotating counterclockwise by an angle x from the positive real axis. Similarly, e^(i*y) represents a point on the unit circle, rotating counterclockwise by an angle y. When these two complex numbers are multiplied together, their angles add up, resulting in a new complex number represented by e^(i*x+i*y). This new complex number also lies on the unit circle. The equation being discussed focuses on the real part (Re) of this new complex number. It expresses the real part as a product of the real and imaginary parts of the original two complex numbers e^(i*x) and e^(i*y). The real part of a complex number represents the projection of the complex number onto the real axis. In geometric terms, it corresponds to the x-coordinate of the point represented by the complex number. By using the equation, one can calculate the real part of e^(i*x+i*y) without needing to compute the exponentials directly. This can be particularly useful in certain mathematical problems and applications where the real part is of interest instead of the full complex number. Overall, the equation provides a relationship between the real parts of the individual complex numbers and their product, allowing for a more simplified representation of the result.$

$\mathrm{Explain}\left(\mathrm{\Re }\left(\mathrm{\sigma }\right)<0\right)$

$\mathrm{Explain}\left(\mathrm{continue}\right)$

$\mathrm{Explain}\left(''The\; Maple\; command\; simplify''\right)$

$''The\; Maple\; command\; "simplify"\; is\; used\; to\; simplify\; mathematical\; expressions.\; It\; uses\; various\; algorithms\; and\; techniques\; to\; transform\; complex\; expressions\; into\; simpler\; ones\; that\; are\; more\; manageable\; and\; easier\; to\; understand\; or\; compute.\; The\; commands\; take\; the\; form:\; simplify(expression)\; Here,\; \text{'}expression\text{'}\; is\; the\; mathematical\; expression\; you\; want\; to\; simplify.\; For\; instance,\; you\; can\; do:\; simplify(y^3\; +\; 3*y^2\; +\; 3*y\; +\; 1\; -\; (y+1)^3)\; Maple\; will\; return\; that\; this\; expression\; simplifies\; to\; 0\; because,\; indeed,\; the\; two\; sides\; of\; the\; subtraction\; are\; equal.\; It\; can\; simplify\; all\; sorts\; of\; mathematical\; expressions,\; including\; those\; involving\; polynomials,\; trigonometric\; functions,\; exponentials,\; logarithms,\; and\; more.\; Note\; though\; that\; what\; is\; understood\; as\; a\; "simplified"\; from\; can\; depend\; on\; the\; context,\; in\; some\; cases\; additional\; parameters\; may\; be\; necessary\; to\; guide\; the\; simplification\; process\; towards\; a\; desired\; form.''$

$\mathrm{Explain}\left(\mathrm{continue}\&comma;\mathrm{model}=\mathrm{ChatGPT}\right)$

$The Maple command simplify is used to simplify mathematical expressions or equations in Maple, a mathematical software. When you have a complex expression or equation, simplify allows you to obtain a more concise and understandable form by performing algebraic manipulations, simplifications, and expansions. The simplify command can handle various types of expressions, such as polynomials, trigonometric functions, logarithms, exponentials, and more. It applies a set of predefined rules and simplification techniques to reduce the expression to a simpler form. These rules involve basic algebraic operations, properties of functions, and identities. Simplify can be used in different situations, such as: 1. Simplifying algebraic expressions: It can combine like terms, factor polynomials, expand brackets, and simplify fractions to obtain the most compact representation of an expression. 2. Simplifying trigonometric expressions: It can simplify trigonometric identities, reduce trigonometric functions to their simplest form, and convert trigonometric expressions into alternative forms. 3. Simplifying logarithmic and exponential expressions: It can simplify logarithmic or exponential equations, simplify powers and exponents, and apply logarithmic and exponential identities. 4. Simplifying rational expressions: It can simplify rational functions by canceling common factors in the numerator and denominator, expanding and factoring expressions, and reducing fractions. In addition to simplifying expressions, you can also use the simplify command to simplify equations. It can manipulate equations by moving terms to one side, combining like terms, applying properties of equality, or solving equations for a specific variable. Overall, the simplify command in Maple is a powerful tool for performing mathematical simplifications, making expressions or equations more manageable, and helping to identify patterns or relationships in mathematical problems.$

$\mathrm{Explain}\left(''Weight\; of\; a\; W10X54\; beam?''\right)$

$''A\; W10X54\; beam\; refers\; to\; a\; beam\; that\; is\; a\; wide\; flange\; shape\; (signified\; by\; the\; "W"),\; that\; is\; approximately\; 10\; inches\; deep\; (the\; "10"\; part\; of\; the\; label)\; and\; weighs\; 54\; pounds\; per\; foot\; (signified\; by\; the\; "54").\; These\; abbreviations\; and\; numbers\; are\; part\; of\; a\; standardized\; system\; used\; in\; the\; structural\; steel\; industry\; to\; denote\; the\; sizes,\; shapes\; and\; weights\; of\; steel\; beams\; and\; other\; sections.''$

$\mathrm{Explain}\left(\mathrm{further}\right)$

$A W10X54 beam is a type of beam used in the construction and civil engineering industries. The term "W10X54" is a standard designation in the American Institute of Steel Construction (AISC) system, used to specify the size and weight of the beam. In W10X54, "W" refers to the type of the beam which is wide-flange. Wide-flange beams have parallel inner and outer flange surfaces and are also commonly referred to as "H" beams. The number 10 represents the nominal depth of the beam in inches. Nominal depth is a standard dimension referring to the breadth-depth ratio of the beam. The number 54 refers to the weight of the beam. Specifically, a W10X54 beam weighs 54 pounds per linear foot. So, if the beam was 10 feet long, it would weigh 540 pounds. This weight includes the weight of the steel beam itself and does not account for any loading (other weight) that the beam may be supporting. This identification system allows engineers and construction workers to quickly understand the properties of a beam and determine if it is suitable for a particular usage without having to refer to additional tables or literature.$

The OpenAI website.

The NaturalLanguage:-Explain command was introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.