# 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.
# import Expression classes needed to build the expression
from proveit import ExprTuple, a, b, c, k
from proveit.core_expr_types import alpha_k
from proveit.numbers import Add, Interval, Sum, one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = [k]
expr = ExprTuple(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, c)), Add(Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(a, b)), Sum(index_or_indices = sub_expr1, summand = alpha_k, domain = Interval(Add(b, one), c))))

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}^{c} \alpha_{k}, \left(\sum_{k = a}^{b} \alpha_{k}\right) + \left(\sum_{k = b + 1}^{c} \alpha_{k}\right)\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1, 2
1Operationoperator: 10
operand: 5
2Operationoperator: 37
operands: 4
3ExprTuple5
4ExprTuple6, 7
5Lambdaparameter: 29
body: 8
6Operationoperator: 10
operand: 13
7Operationoperator: 10
operand: 14
8Conditionalvalue: 20
condition: 12
9ExprTuple13
10Literal
11ExprTuple14
12Operationoperator: 26
operands: 15
13Lambdaparameter: 29
body: 16
14Lambdaparameter: 29
body: 17
15ExprTuple29, 18
16Conditionalvalue: 20
condition: 19
17Conditionalvalue: 20
condition: 21
18Operationoperator: 32
operands: 22
19Operationoperator: 26
operands: 23
20IndexedVarvariable: 24
index: 29
21Operationoperator: 26
operands: 27
22ExprTuple34, 36
23ExprTuple29, 28
24Variable
25ExprTuple29
26Literal
27ExprTuple29, 30
28Operationoperator: 32
operands: 31
29Variable
30Operationoperator: 32
operands: 33
31ExprTuple34, 39
32Literal
33ExprTuple35, 36
34Variable
35Operationoperator: 37
operands: 38
36Variable
37Literal
38ExprTuple39, 40
39Variable
40Literal