Lisp格式多项式
我将稀疏多项式表示为(系数,对)列表。例如:Lisp格式多项式,lisp,common-lisp,Lisp,Common Lisp,我将稀疏多项式表示为(系数,对)列表。例如: '((1 2) (3 6) (-20 48)) => x^2 + 3x^6 - 20x^48 我不熟悉Lisp格式,但是遇到了一些非常漂亮的工具,比如(format nil“~:[+~;-~]”(>0系数))以文本形式获取系数的符号(我知道,这可能不是惯用法) 但是,格式化单个术语时会出现某些显示问题。例如,以下各项均应为真: (1 0) => 1x^0 => 1 (reducible) (1 1) => 1x^1 =
'((1 2) (3 6) (-20 48)) => x^2 + 3x^6 - 20x^48
我不熟悉Lisp格式,但是遇到了一些非常漂亮的工具,比如(format nil“~:[+~;-~]”(>0系数))
以文本形式获取系数的符号(我知道,这可能不是惯用法)
但是,格式化单个术语时会出现某些显示问题。例如,以下各项均应为真:
(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)
我想知道是否有一种方法可以在不使用大量if
或cond
宏的情况下实现这一点-一种只使用单个格式
模式的方法。除了“美化”术语(FormatPolynomialHelper3中的最后一行应该可以做到这一点)之外,一切都正常
编辑:正确地说输出不应该包含逻辑。也许我问的问题太具体了。下面是正确格式化多项式的逻辑-但我正在寻找更干净、更可读、更具lisp风格的东西(这只是我编写lisp的第三天)
回答:
(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)))
CL-USER 14 > (write-polynomial '((1 2) (3 6) (-20 48)))
-20x^48 + 3x^6 + x^2
我不会将此逻辑放入格式
语句中。仅当您希望加密代码或为自己创建更多维护工作时。好的Lisp代码是自文档的<代码>格式语句从不自我记录
在打印之前,我首先简化多项式。例如,删除每个乘以零的项
((0 10) (1 2)) -> ((1 2))
然后,如果乘数为1,则可以在正常的条件下
或情况下
语句中进行测试
另外,请确保不要使用带有自制数据结构的汽车
,CDR
,第一个
,第二个
。多项式的组件应该主要通过隐藏大部分实现细节的自文档化函数来访问
我将不使用格式编写它
:
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)))
CL-USER 14 > (write-polynomial '((1 2) (3 6) (-20 48)))
-20x^48 + 3x^6 + x^2
示例使用:
(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)))
CL-USER 14 > (write-polynomial '((1 2) (3 6) (-20 48)))
-20x^48 + 3x^6 + x^2
术语'(10)
和'(20)
的格式分别为x^0
和2x^0
,它们应该是1
和2
。