Lisp Formatting Polynomial

我代表稀疏多项式作为列表（系数，对）。 例如：

'((1 2) (3 6) (-20 48)) => x^2 + 3x^6 - 20x^48

我是新来的Lisp的格式，但都遇到了一些非常漂亮的工具，如(format nil "~:[+~;-~]" (> 0 coefficient))以获得系数为文本的符号（我知道，这可能不地道）。

然而，单一的格式条款时，也有一定的显示问题。 例如，下面的应该都是真实的：

(1 0) => 1x^0 => 1    (reducible)
(1 1) => 1x^1 => x    (reducible)
(1 2) => 1x^2 => x^2  (reducible)
(2 0) => 2x^0 => 2    (reducible)
(2 1) => 2x^1 => 2x   (reducable)
(2 2) => 2x^2 => 2x^2 (this one is okay)

我不知道是否有一种方法可以做到这一点没有一个大系列if还是cond宏-一种只用一个做到这一点format模式。 一切正常，但“美化”的条款（最后一致FormatPolynomialHelper3应该这样做）。

(defun FormatPolynomial (p)
    "Readably formats the polynomial p."
    ; The result of FormatPolynomialHelper1 is a list of the form (sign formatted),
    ; where 'sign' is the sign of the first term and 'formatted' is the rest of the
    ; formatted polynomial. We make this a special case so that we can print a sign
    ; attached to the first term if it is negative, and leave it out otherwise. So,
    ; we format the first term to be either '-7x^20' or '7x^20', rather than having
    ; the minus or plus sign separated by a space.
    (destructuring-bind (sign formatted-poly) (FormatPolynomialHelper1 p)
        (cond
            ((string= formatted-poly "") (format nil "0"))
            (t                           (format nil "~:[~;-~]~a" (string= sign "-") formatted-poly)))))

; Helpers

(defun FormatPolynomialHelper1 (p)
    (reduce #'FormatPolynomialHelper2 (mapcar #'FormatPolynomialHelper3 p) :initial-value '("" "")))

(defun FormatPolynomialHelper2 (t1 t2)
    ; Reduces ((sign-a term-a) (sign-b term-b)) => (sign-b "term-b sign-a term-a"). As
    ; noted, this accumulates the formatted term in the variable t2, beginning with an
    ; initial value of "", and stores the sign of the leading term in the variable t1.
    ; The sign of the leading term is placed directly before the accumulated formatted
    ; term, ensuring that the signs are placed correctly before their coefficient. The
    ; sign of the the leading term of the polynomial (the last term that is processed)
    ; is available to the caller for special-case formatting.
    (list
        (first t2)
        (format nil "~@{~a ~}" (second t2) (first t1) (second t1))))

(defun FormatPolynomialHelper3 (tm)
    ; Properly formats a term in the form "ax^b", excluding parts of the form if they
    ; evaluate to one. For example, 1x^3 => x^3, 2x^1 => 2x, and 3x^0 => 3). The list
    ; is in the form (sign formatted), denoting the sign of the term, and the form of
    ; the term state above (the coefficient have forced absolute value).
    (list
        (format nil "~:[+~;-~]" (> 0 (first tm)))
        (format nil "~a~@[x^~a~]" (abs (first tm)) (second tm))))

编辑 ：这是正确的说，输出不应该包含的逻辑。 也许我是问太具体的我的问题一个问题。 下面是正确格式的多项式的逻辑 - 但我正在寻找的东西更清洁，更具可读性，更加口齿不清，地道的（这只是我的第三天写LISP）。

(defun FormatPolynomialHelper3 (tm)
    ; Properly formats a term in the form "ax^b", excluding parts of the form if they
    ; evaluate to one. For example, 1x^3 => x^3, 2x^1 => 2x, and 3x^0 => 3). The list
    ; is in the form (sign formatted), denoting the sign of the term, and the form of
    ; the term state above (the coefficient have forced absolute value).
    (list
        (format nil "~:[+~;-~]"   (> 0 (first tm)))
        (cond
            ((= 0 (second tm))      (format nil "~a" (abs (first tm))))
            ((= 1 (abs (first tm))) (cond
                ((= 1 (second tm))  (format nil "x"))
                (t                  (format nil "x^~a" (second tm)))))
            ((= 1 (second tm))      (format nil "~ax" (abs (first tm))))
            (t                      (format nil "~ax^~a" (abs (first tm)) (second tm))))))

Answer 1:

答 ：

我不会把这个逻辑到FORMAT语句。 只有当你想加密的代码或为自己创造更多的维护工作。 良好的Lisp代码是自我记录。 FORMAT语句是从来没有自我记录。

在打印之前我会先简化多项式。 例如去除每其乘以零术语。

((0 10) (1 2)) -> ((1 2))

然后，如果乘数为1能够以正常的被测试COND或CASE语句。

另外，还要确保你从来不使用CAR ， CDR ， FIRST ， SECOND与自制的数据结构。 多项式的组件应该主要由自我记录功能最隐藏的实施细节进行访问。

我会写它没有FORMAT ：

示例代码 ：

(defun term-m (term)
  (first term))

(defun term-e (term)
  (second term))

(defun simplify-polynomial (p)
  (remove-if #'zerop (sort p #'> :key #'term-e)
             :key #'term-m))

(defun write-term (m e start-p stream)
  ; sign or operator
  (cond ((and (minusp m) start-p)
         (princ "-" stream))
        ((not start-p)
         (princ (if (plusp m) " + " " - ") stream)))
  ; m
  (cond ((not (= (abs m) 1))
         (princ (abs m) stream)))
  (princ "x" stream)
  ; e
  (cond ((not (= 1 e))
         (princ "^" stream)
         (princ e stream))))

(defun write-polynomial (p &optional (stream *standard-output*))
  (loop for (m e) in (simplify-polynomial p)
        for start-p = t then nil
        do (write-term m e start-p stream)))

使用示例 ：

CL-USER 14 > (write-polynomial '((1 2) (3 6) (-20 48)))
-20x^48 + 3x^6 + x^2

文章来源: Lisp Formatting Polynomial