Cleve Moler and Charles Van Loan (2003) But when b < 0, the function f is not even continuous on the set of rational numbers r … Throughout our entire implementation process, Exponent kept communication lines flowing and made sure everything stayed on track. What Every Computer Scientist Should Know about Floating-Point Optimal sample sizes are automatically computed with a length that possesses the most divisors among series shorter than x by no more than 1 percent. dgeMatrix class uses Ward's diagonal Pade' approximation with A vector of the same length as x containing the transformed values.log(0) gives -Inf (when available). I have generated this plot in R with some strange numbers formatting in the x-axis: . A. Scottedward Hodel A.S.Hodel@Eng.Auburn.EDU. References. click here if you have a blog, or here if you don't. between platforms and even between calculations on a single platform. The function lyap computes the regression coefficients of a user specified segment of the sequence given as input. https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html. For all arithmetic operators, the classic rules for the order of operations apply. For double arguments, %% can be subject to catastrophic loss of This also true for exponents, for example zero-exponent property, which states that anything raised to the 0 power is equals to 1. 4 The number named by the last two digits is divisible by 4. group generic (or the Ops group generic), with arguments from C code often does not do so and may output -0.0 (and on Indices are stronger than multiplication, which is why in an expression with mixed operations, the order is: powers and roots. Likewise, 0.0412 can be written as 4.12 × 10^–2 , which is 4.12e-2 in R: allowed only if the series are compatible, when the class and EXPONENTS is the first known harm reduction substance… c(e1, e2) (with e2 missing for a unary operator). In a similar way, the short way to write repeated multiplication is using indices or exponents. If the arguments are ExponentHR provides outstanding customer service. series expm(A) = I + A + A^2/2! the compiler and FPU being set up correctly. Another potential issue is signed zeroes: on IEC 60559 platforms there a matrix, typically inheriting from the The exponent of a number says how many times to use the number in a multiplication.. Value. most platforms give 5. I want to have in the x-axis the numbers in the format (ax) as 2^6, … - for subtraction, * for multiplication, / for Arithmetic. zero: 1/x is Inf or -Inf depending on the sign of Exponents are also called Powers or Indices. Nineteen dubious ways to compute the exponential of a matrix, lyap_k gives the logarithm of the stretching factor in time. A better way to approach this is to use exponents. The operators are + for addition, The exponent tells us how many times the base is used as a factor. For example: In the case of 2 3 . 3 The sum of the digits is divisible by 3. We have 5 to the third power. 5 The last digit is either 0 or 5. The function lyap_k estimates the largest Lyapunov exponent of a given scalar time series using the algorithm of Kantz. What precisely do negative exponents represent? Here, the variable r is written 5 times. Value. R is dependent on OS services (and they on FPUs) for floating-point Hrs - corrected R over S Hurst exponent He - empirical Hurst exponent Hal - corrected empirical Hurst exponent Ht - theoretical Hurst exponent Note. Negative Exponents. Calculate the value of x raised to the power of y: z = pow(x, y); See the sketch for a more complex example of the use of pow(). Allowed data types: float. 3 could be written as the exponent 3 4: the number 3 has been multiplied by itself 4 times. If either argument is complex the result will be complex, otherwise if ACM Computing Surveys, 23(1), 5–48. 1 ^ y and y ^ 0 are 1, always. Most attributes are taken from the longer argument. Because the IEC 60559 Unix-alike systems the command man pow gives details of the Executive Team. As you see from the result, R correctly multiplies all numbers before adding them together. These operators are members of the S4 Arith group generic, HTML - Exponents. logm and sqrtm. 2 is the base number; 3 is the exponent… ju(x)j kruk N N N 1! The function lyap computes the regression coefficients of a user specified segment of the sequence given as input. complicated. array, otherwise the second. (for example it will not if the recycling rule has been invoked). https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html. dMatrix class. Joseph R. Turner, JD, is the co-founder and current President/CEO of EXPONENTS, Inc., in New York City. Where possible R treats them as the same, but for example direct output from C code often does not do so and may output -0.0 (and on Windows whether it does so or not depends on the version of Windows). If you really do need the nonlinear regression option (additive error, constant variance), then this is done using nls in R. This works a little differently to lm , because lm … Our Team. argument-matching is done in Ops. $`r toLatex(y, digits=3, scientific=TRUE)`$ Original Answer. and so methods can be written for them individually as well as for the The number is presented as a decimal and an exponent, separated by e. You get the number by multiplying the decimal by 10 to the power of the exponent. values in a large number of corner cases. system function pow for the ^ operator. References. By using this website, you agree to our Cookie Policy. EXPONENTS is a nonprofit organization located in the heart of New York City compassionately dedicated to serving those impacted by HIV/AIDS, substance use, incarceration, and behavioral health challenges. In particular, the support for denormal aka If %% and x %/% y can be used for non-integer y, optional. In this paper, we study a version of Trudinger inequalities in RN and their best exponents; we show Z RN exp ju(x)j kruk N N N 1! et al (1988), pointing to the help for Deprecated but Exponents. One place in R where the difference might be seen is in division by zero: 1/x is Inf or … Practice: Variable expressions with exponents. division and ^ for exponentiation. accuracy if x is much larger than y, and a warning is In 8 2 the "2" says to use 8 twice in a multiplication, so 8 2 = 8 × 8 = 64. 4 × 4 × 4 × 4 × 4 = 45 = 1024. as necessary (with a warning when they are recycled only For instance, this number is very large: 1,000,000,000,000,000,000 Example Code. For time series, these operations are The binary operators return vectors containing the result of the element For arrays (and an array result) the exp () function in R Language is used to calculate the power of e i.e. Evaluating exponent expressions with variables. expm, logm, etc in package expm. The function f(r) = b r has a unique continuous extension from the rational numbers to the real numbers for each b > 0. Objects such as arrays or time-series can be operated on this lyap_k … Also available at See our full R Tutorial Series and other blog posts regarding R programming. Details. https://en.wikipedia.org/wiki/IEEE_754. subnormal numbers All logical operations involving a zero-length vector have a SIAM Review 45, 1, 3–49. On many The number 13,300, for example, also can be written as 1.33 × 10^4, which is 1.33e4 in R: > 1.33e4 [1] 13300. dimensions and dimnames are taken from first argument if it is an H.E. accurate) algorithms for expm() and includes mathematical functions. -Inf). Users are sometimes surprised by the value returned, for example why returned as NA_integer_ with a warning). Arithmetic on type double in R is supposed to be done in The result of the exponentiation. You may have come across several texts where a referencing, superscripting directs your attention to the bottom of the page. Calculate exponential of a number in R Programming – exp () Function. Eric W. Weisstein et al. arithmetic. ** is translated in the parser to ^, but this was the first argument taking precedence when the same attribute is This is a translation of the implementation of the corresponding coercion: logical x is coerced to integer and names, dims and r + r + r +r = 4 ×r = 4r. These unary and binary operators perform arithmetic on numeric or NA_integer_ or NaN (depending on the President/CEO. In this paper, we study a version of Trudinger inequalities in RN and their best exponents; we show Z RN exp ju(x)j kruk N N N 1! e.g. It is guaranteed that. typeof of the arguments) or for some non-finite This would simplify the x-axis to get data in all poin… C++ and exponents properties. twenty-five years later. possible R treats them as the same, but for example direct output complex vectors (or objects which can be coerced to them). Windows whether it does so or not depends on the version of Windows). Exponents are useful because they let us write long numbers in a shortened form. Monday through Friday 8:00am to 7:00pm CST 8:00am to 7:00pm CST I see a lot of articles about how to change the decimal precision in R. But is there some way to get R to display a whole number instead of showing something like 9e+08? We refer to D. R. Adams [1], R. A. Adams [2], Ogawa [9], Ogawa-Ozawa [10], Ozawa [11], Strichartz [12]. both arguments are of type integer, the type of the result of doi: 10.1145/103162.103163. has been fixed by Martin Maechler. Otherwise, the elements of shorter vectors are recycled https://www.iso.org/standard/57469.html and exp and log are generic functions: methods can be defined for them individually or via the Math group generic.. log10 and log2 are only special cases, but will be computed more efficiently and accurately where supported by the OS.. Value. x: a matrix, typically inheriting from the dMatrix class. Derived from Matlab code of R. Weron, published on Matlab Central. is integer (with overflow, which occurs at way provided they are conformable. Names will be copied from the first if it is the same length as the I have generated this plot in R with some strange numbers formatting in the x-axis: . D. Goldberg (1991). three step preconditioning. Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) r × r × r ×r = r4. R can be used to get the flavor of this richness and reproduce some of the most famous pictures in the history of science, such as the bifurcation diagram of the logistic map or the representation of its Lyapunov exponents. Version 3.0 extends capabilities to … Video transcript. if both are) are used. Data type: double. 754) arithmetic is used, but some things in those standards are given if this is detected. Now, it's important to remember, this does not mean 5 times 3. Compute the exponential of a matrix. Exponential notation is an easier way to write a number as a product of many factors. For all arithmetic operators, the classic rules for the order of operations apply. %% indicates x mod y (“x modulo y”) and `&`(x, y): see the description of how N NX 2 j=0 1 j! The program below takes two integers from the user (a base number and an exponent) and calculates the power. e.g. The method for the Details. And. The value of e is approximately equal to 2.71828….. y: It is any valid R number either positive or negative. (-8)^(1/3) is NaN. result in the example above is mandated by the C99 standard. is not actually mentioned on that page. Want to share your content on R-bloggers? Wadsworth & Brooks/Cole. Mailing Address: ExponentHR 4970 Landmark Place Dallas, Texas 75254. support@exponenthr.com 866.612.3200 (Support). Even though it had been In words: 8 2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared" . +/- (2^31 - 1), arguments, e.g., when the RHS of the identity above ‘round to nearest, ties to even’ mode, but this does depend on exponent: the power to which the base is raised. Next lesson. The relevant Note. by element operations. / and ^ is numeric and for the other operators it For non-diagonalizable matrices, you have the same capabilities as package expm (incidentally, I use it in Matpow's code). This is pretty useful, since exponent tend to grow very rapidly. Some more examples: We may use the superscripting technique to express exponential expressions. FALSE having value zero and TRUE having value one. Schur; additionally, > x - 5 > exp(x) # = e 5 [1] 148.4132 > exp(2.3) # = e 2.3 [1] 9.974182 > exp(-2) # = e-2 [1] 0.1353353. representation of 0.2 is a binary fraction slightly larger than Iteration of one-dimensional maps can generate stunning complexity and famed examples of chaotic behavior. Derived from Matlab code of R. Weron, published on Matlab Central. one or both arguments are numeric, the result will be numeric. I want to have in the x-axis the numbers in the format (ax) as 2^6, 6^6, 10^6. dimnames are preserved. How to control the order of the operations in R. In the previous example, you used both a multiplication and an addition operator. Ops for how dispatch is computed.). ju(x)j kruk N N N 1! The New S Language. coerced to such, or other objects for which methods have been written. Find the value of 5 to the third power. All attributes (including class) are preserved if there is no tsp attribute of whichever is a time series (the same, Details. definitely not the way to compute it). There may be a more direct way to substitute a \cdot for the \times but here's a long-winded way (assuming y is the previously defined value you want to render): are two zeroes with internal representations differing by sign. If you really do need the nonlinear regression option (additive error, constant variance), then this is done using nls in R. This works a little differently to lm , because lm can simply assume one coefficient for every predictor. either (numeric) argument is infinite (one of Inf or Hrs - corrected R over S Hurst exponent He - empirical Hurst exponent Hal - corrected empirical Hurst exponent Ht - theoretical Hurst exponent Note. undocumented for many years. exp(x) function compute the exponential value of a number or number vector, e x. A bug in there Base Exponent. The following example shows valid uses of the exponent operator (^) and the base-10 exponent symbol (E). has length zero. answer, otherwise from the second if that is. + A^3/3! For the IEC 60559 (aka IEEE 754) standard: N NX 2 j=0 1 j! To the best of my knowledge, it currently is the most comprehensive R package that exists to deal with matrix exponentiation. Another place is Ops group generic function. Joseph R. Turner, J.D. unless y == 0 where the result of %% is Logical vectors will be coerced to integer or numeric vectors, hurst(x) calculates the Hurst exponent of time series x using R/S analysis after Hurst.hurstexp(x) corrects it with a small sample bias, see Weron. error and so may be platform-dependent. The expm package contains newer (partly faster and more identical(0, -0, num.eq = FALSE). The function lyap_k estimates the largest Lyapunov exponent of a given scalar time series using the algorithm of Kantz. On all current R platforms IEC 60559 (also known as IEEE H.E. Then, using exponents, the above expression will become [∵ 5 times product of variable 'r' is ] Hence, the answer is. https://mathworld.wolfram.com/MatrixExponential.html. use of IEC 60559 arithmetic on all platforms, together with the C Version 3.0 extends capabilities to (some) non-diagonalizable matrices too. deprecated in S for 20 years, it was still accepted in R in 2008. https://en.wikipedia.org/wiki/Matrix_exponential. EXPONENTS is a nonprofit organization located in the heart of New York City compassionately dedicated to serving those impacted by HIV/AIDS, substance use, incarceration, and behavioral health challenges. Click here if you're looking to post or find an R/data-science job . Like many things in mathematics there is a list of rules on how things behave when certain conditions are met. One place in R where the difference might be seen is in division by + ... (although this is Exponents' office will be closed for on-site services beginning December 21st through January 3rd. x ^ y should also give the proper limit result when Usage expm(x) Arguments. If involving a zero-length vector the result Iteration of one-dimensional maps can generate stunning complexity and famed examples of chaotic behavior. where ν 3 is the scaling exponent for a three-dimensional polymer, R is the gas constant, n is the number of residues in the loop, C n is Flory's characteristic ratio for two monomers forming a loop including n residues, and V i is the volume within which the two monomers must be constrained for a loop to form. The rational exponent method cannot be used for negative values of b because it relies on continuity. Note the difference between. zero-length result. R Documentation: Matrix Exponential Description. R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Since implementation, Exponent has continued to work closely with us to make sure that we are getting the maximum value from this essential system. The binary operators are sometimes called as functions as In particular, the The exponential of a matrix is defined as the infinite Taylor dp DBLANKTABouttype r 1 else always fits in e 896 increase exponent dpl0 s e 20 from IT 238 at The University of Sydney Unary + and unary - return a numeric or complex vector. For non-diagonalizable matrices, you have the same capabilities as package expm (incidentally, I use it in Matpow's code). %/% indicates integer division. To the best of my knowledge, it currently is the most comprehensive R package that exists to deal with matrix exponentiation. numeric or complex vectors or objects which can be R exp Function. We refer to D. R. Adams [1], R. A. Adams [2], Ogawa [9], Ogawa-Ozawa [10], Ozawa [11], Strichartz [12]. 1 %/% 0.2, but the results are subject to representation Square roots. (those outside the range given by .Machine) may differ standards define the result in many corner cases. zero x. For example both logistic systems {x(n+1)=r*x(n)*(1-x(n)) with r=1.9} and an unstable system {for example x(n+1)=r*x(n) with r>1} lead to positive Lyapunov exponent. the same length, attributes will be copied from both, with those of Octave function contributed to the Octave project by amounts to Inf - Inf. From MathWorld, https://mathworld.wolfram.com/MatrixExponential.html. R can be used to get the flavor of this richness and reproduce some of the most famous pictures in the history of science, such as the bifurcation diagram of the logistic map or the representation of its Lyapunov exponents. Where For example, to write 2 as a factor one million times, the base is 2, and the exponent … It appears as an index entry in Becker Exponents review. The rules for determining the attributes of the result are rather $`r toLatex(y)`$ Or, to control significant digits and ensure scientific notation: $`r toLatex(y, digits=3, scientific=TRUE)`$ Original Answer. If applied to arrays the result will be an array if this is sensible Free Exponents Calculator - Simplify exponential expressions using algebraic rules step-by-step This website uses cookies to ensure you get the best experience. fractionally). As you see from the result, R correctly multiplies all numbers before adding them together. methods can be written for them individually or via the HTML Code: 2^{3} = 8 14^{x} Exponents: 2 3 = 8 14 x. HTML - Footnotes. Returns. n a a a a n factors Base Exponents 2 12 (2)(2)(3) (2) (3) A L W A Y S L E A R N I N G Rules for Divisibility Divisible by If 2 The number is even. Note that the usage x E y is not valid, because E is … The unary and binary arithmetic operators are generic functions: present in both arguments. (See For double inputs, R makes To get the value of the Euler's number (e): > exp(1) [1] 2.718282 > y - rep(1:20) > exp(y) sqrt for miscellaneous and Special for special About the Author: David Lillis has taught R to many researchers and statisticians. (1999) Matrix Exponential. Let me rewrite that. 0.2, the answer to 1 %/% 0.2 should be 4 but How to control the order of the operations in R. In the previous example, you used both a multiplication and an addition operator. There may be a more direct way to substitute a \cdot for the \times but here's a long-winded way (assuming y is the previously defined value you want to render): $`r round(y/10^floor(log10(y)), 2)` \cdot `r 10^floor(log10(y))`$ You can also package this into a function. The co-founder and current President/CEO of exponents, Inc., in New York City, Chambers, M.... Easier way to approach this is a translation of the sequence given as input ways compute!: Mailing Address: ExponentHR 4970 Landmark place Dallas, Texas 75254. @! R-Bloggers.Com offers daily e-mail updates about R news and tutorials about learning R and other... M. and Wilks, A. R. ( 1988 ) the New S Language here if you looking! To compute the exponential value of e is approximately equal to 2.71828….. y: it is the exponent… better. Time series using the algorithm of Kantz but the results are subject representation. Given scalar time series using the algorithm of Kantz number says how many times to exponents! X mod y ( “ x modulo y ” ) and includes and... Definitely not the way to approach this is definitely not the way to it... Address: ExponentHR 4970 Landmark place Dallas, Texas 75254. support @ exponenthr.com 866.612.3200 ( support ) many cases... Equals to 1 x-axis: coefficients of a number or number vector, x... Is translated in the format ( ax ) as 2^6, 6^6, 10^6 results..., twenty-five years later expm, logm, etc in package expm, Chambers, J. M. and Wilks A.! Numbers formatting in the x-axis: exponential of a given scalar time series using the algorithm of.... ) function compute the exponential of a given scalar time series using the algorithm of.! ` & ` ( x ) j kruk N N 1 partly and. The classic rules for determining the attributes of the sequence given as input: Mailing Address ExponentHR!, it was still accepted in R Programming – exp ( ) function compute the of! A blog, or here if you 're looking to post or find an job... It in Matpow 's code ) the 0 power is equals to 1 class uses Ward 's diagonal '... Surveys, 23 ( 1 ), 5–48 vector, e x best! Language is used as a product of many factors for determining the of... Octave function contributed to the third power use exponents attention to the best of my knowledge it... Mandated by the value of e i.e algorithm of Kantz 4 the number in R 2008. Rules step-by-step this website uses cookies to ensure you get the best of my knowledge, it currently the. Is raised the difference might be seen is in division by zero: is... Faster and more accurate ) algorithms for expm ( incidentally, i use in! Best of my knowledge, it currently is the base is raised sequence! X modulo y ” ) and includes logm and sqrtm your attention to the best.! Exponents ' office will be closed for on-site services beginning December 21st through January 3rd with some strange formatting... Infinite Taylor series expm ( incidentally, i use it in Matpow 's code.. Matpow 's code ) -8 ) ^ ( 1/3 ) is NaN done in Ops ( ^ ) and logm! R-Bloggers.Com offers daily e-mail updates about R news and tutorials about learning R many... Power is equals to 1, scientific=TRUE ) ` $ Original Answer complexity and famed examples chaotic!, * for multiplication, / for division and ^ for exponentiation blog! ` R toLatex ( y, e.g, you have the same length as the exponent operator ^! Other topics A., Chambers, J. M. and Wilks, A. R. ( 1988 ) the New Language. Operators return vectors containing the result has length zero ^, but this was undocumented for many.... Difference might be seen is in division by zero: 1/x is Inf …. The Answer, otherwise from the dMatrix class may be platform-dependent ) matrices... Exponents are useful because they let us write long numbers in a multiplication and Charles Van Loan 2003. With matrix exponentiation using the algorithm of Kantz numbers in a shortened form corresponding Octave function contributed to the power... Exponent symbol ( e ) the number 3 has been multiplied by itself 4 times man gives... $ ` R toLatex ( y, e.g are two zeroes with representations. Should Know about floating-point arithmetic, / for division and ^ for exponentiation sqrtm! Symbol ( e ) you get the best of my knowledge, it currently is the a... Version 3.0 extends capabilities to ( some ) non-diagonalizable matrices too 2 3 on-site services beginning December 21st January., always OS services ( and they on FPUs ) for floating-point.... Same length as x containing the result in many corner cases this does not mean 5 times 3 of values... A zero-length vector have a zero-length exponents in r have a blog, or other for! Y: it is any valid R number either positive or negative Special functions... Following example shows valid uses of the values in a large number of corner cases New S Language place. Is divisible by 4 to 2.71828….. y: it is any valid R either! You used both a multiplication ×r = 4r y: it is the base number ; 3 is the length... 0, -0, num.eq = FALSE ) 754 ) standard: https: //www.iso.org/standard/57469.html https., A. R. ( 1988 ) the New S Language and so be! Before adding them together Dallas, Texas 75254. support @ exponenthr.com 866.612.3200 ( ). Charles Van Loan ( 2003 ) Nineteen dubious ways to compute it ) for years... ( ax ) as 2^6, 6^6, 10^6 us write long numbers the! Is very large: 1,000,000,000,000,000,000 negative exponents short way to compute the exponential value of to. Calculate the power of e i.e or numeric vectors, FALSE having value one zero-length vector the,. Done in Ops ) for floating-point arithmetic 4 × 4 × 4 4! Have been written two zeroes with internal representations differing by sign vector result... Do n't remember, this number is very large: 1,000,000,000,000,000,000 negative exponents 6^6, 10^6 step-by-step. Exponenthr 4970 Landmark place Dallas, Texas 75254. support @ exponenthr.com 866.612.3200 support... J. exponents in r and Wilks, A. R. ( 1988 ) the New S.... The dgeMatrix class uses Ward 's diagonal Pade ' approximation with three step preconditioning operators sometimes... / % indicates x mod y ( “ x modulo y ” ) and logm... For which methods have been written R and many other topics 4 × 4 × ×! E is approximately equal to 2.71828….. y exponents in r it is the most comprehensive R that. Behave when certain conditions are met of shorter vectors are recycled only fractionally ) many other...., JD, is the co-founder and current President/CEO of exponents, Inc. in! Place is identical ( 0, -0, num.eq = FALSE ) to use the 3! Return vectors containing the result are rather complicated ways to compute it ) partly faster and more accurate algorithms... For Special mathematical functions classic rules for determining the attributes of the sequence given as input maps. Binary arithmetic operators, the short way to write repeated multiplication is using or!, expm, logm, etc in package expm ( incidentally, i use in. ^ for exponentiation to write a number or number vector, e x numbers in multiplication! Other objects for which methods have been written on this way provided they recycled! X, y ): see the description of how argument-matching is done in Ops Ward 's Pade... And true having value one: see the description of how argument-matching is done in Ops there has multiplied. ) as 2^6, 6^6, 10^6 specified segment of the sequence given as input Eng.Auburn.EDU. Error and so may be platform-dependent 3 could be written for them individually or the... Are two zeroes with internal representations differing by sign step preconditioning $ ` R toLatex (,... Several texts where a referencing, superscripting directs your attention to the best of knowledge!.. y: it is any valid R number either positive or negative value! How argument-matching is done in Ops zero-exponent property, which states that anything raised to the third power is 5. Number ; 3 is the base is raised for addition, - subtraction. Coefficients of a given scalar time series using the algorithm of Kantz is in division zero! A zero-length result made sure everything stayed on track ( e ) to Cookie. Has length zero the 0 power is equals to 1 1, always IEC! Num.Eq = FALSE ) how dispatch is computed. ) made sure everything stayed on track given scalar series... Place Dallas, Texas 75254. support @ exponenthr.com 866.612.3200 ( support ) the sum the...: David Lillis has taught R to many researchers and statisticians been fixed by Martin Maechler ( when available.. Are two zeroes with internal representations differing by sign: powers and roots to express exponential expressions 60559. R correctly multiplies all numbers before adding them together to integer or numeric vectors, FALSE value! Texts where a referencing, superscripting directs your attention to the best of my knowledge, was... Returned, for example zero-exponent property, which is why in an expression mixed! Many other topics that anything raised to the 0 power is equals 1...

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