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Expression of type Add

from the theory of proveit.numbers.summation

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, k
from proveit.numbers import Add, Interval, Sum, eight, nine, seven, subtract, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = subtract(k, two)
expr = Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(a, seven)), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(eight, nine)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\sum_{k = a}^{7} \left(k - 2\right)\right) + \left(\sum_{k = 8}^{9} \left(k - 2\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 16
operands: 1
1ExprTuple2, 3
2Operationoperator: 5
operand: 7
3Operationoperator: 5
operand: 8
4ExprTuple7
5Literal
6ExprTuple8
7Lambdaparameter: 22
body: 9
8Lambdaparameter: 22
body: 11
9Conditionalvalue: 13
condition: 12
10ExprTuple22
11Conditionalvalue: 13
condition: 14
12Operationoperator: 18
operands: 15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operands: 19
15ExprTuple22, 20
16Literal
17ExprTuple22, 21
18Literal
19ExprTuple22, 23
20Operationoperator: 27
operands: 24
21Operationoperator: 25
operand: 31
22Variable
23Operationoperator: 27
operands: 28
24ExprTuple29, 30
25Literal
26ExprTuple31
27Literal
28ExprTuple32, 33
29Variable
30Literal
31Literal
32Literal
33Literal